Why are helmets and seatbelts required?

Sometime in the 80's, Mike Royko (editorialist for the Chicago Tribune) wrote a piece covering an accident case. (I'm going from memory here.) A car had hit a motorcycle and the fault was clearly the car's. The motorcycle rider suffered pretty bad head injuries and so the car's insurance company was on the hook for substantial damages. The case went to court and the insurance company took this tack:

Since the rider wasn't wearing a helmet, the fact that he sustained severe head injury is largely his own fault. At the time, helmets weren't required in this jurisdiction, but the rider "surely knew the risk" of not wearing a helmet. Why should the car have to pay extra because of his risky behavior.

I don't know how the case came out, but Royko went on to make the point that if the car made his point (and, say, paid only 1/3 of the damages) then it would create a new court tactic called "the seatbelt defense." "Yes, the accident was my fault, but the passenger wasn't wearing a seatbelt, so I'm not totally liable for all the damage."

So my point here is that another reason you have to wear a seatbelt or helmet is because I might smack into you and then you'll sue me for a billion dollars, and I'd like more protection against that.

Law can restrict freedom

Your definition of freedom "I should be able to do anything and everything, if it DOES NOT AT ALL hurt anything or anyone, be it financially, physically, mentally etc." is relevant to the default situation where no relevant regulations exist. However, you live in a society where that freedom is restricted, and you can do anything and everything as long as it does not at all hurt anything or anyone and does not violate any law or regulation of this society.

In the absence of specific law regarding seatbelts, you would be free to not wear a seatbelt as long as it does not hurt anyone else - and if your action does result in harm or injury to someone, you could be liable for the losses, or guilty of (for example) manslaughter by negligence.

However, there can be specific laws that restrict the default freedoms in order to achieve some other social purpose. There are some limitations (constitutional or otherwise) on what freedoms can be restricted, but in general they can be restricted, and often are.

The answer to "why it is compulsory to wear a helmet/seatbelt by law?" is somewhat tautological - it's compulsory because there is a specific law that compels you to do that. There is some justification expected in most societies when passing laws, but any weaknesses in that justification can only be used to argue that this law should not be passed or should be changed, but they don't invalidate the law if it's passed even if the justification is later found to be totally arbitrary, baseless or mistaken.

Multiple other answers provide justifications on how not wearing a seatbelt does harm other people or why the benefits outweigh the drawbacks. However, those are arguments about whether it's a good law, but they are not necessary to establish whether it is a valid law. In the end, the constitution allows the state to restrict your freedom to drive as you please and add some arbitrary conditions (such as wearing a helmet), the lawmakers have chosen to do so and implemented a law following the proper due process - and this makes wearing seatbelts compulsory.

Other answers being good, a lot of pressure to mandate the safety tools and features comes from the insurance business.

When you insure something (be it property or other lawful asset, such as life and health) you are expected to protect the insured asset by all practical means. A certain amount of neglect can be considered insurance fraud.

A seatbelt in the insurance context serves two important purposes:

1. Lowers the risk of death or injuries.
2. Provides forensics traces about the incident conditions (collision speed/direction, etc) that help in determining the liability.

Unfortunately, most other answers here don't have any sources. I'll answer this from the perspective of German lawmakers and translate the appropriate sources, since that's what I am most familiar with.

Germany made it mandatory for cars to have seats belts on the front seats on 1974-01-01, for rear seats on 1979-05-01. Since 1988-01-01 the outer rear seats need to have three-point belts. Trucks need to have seat belts since 1992, buses since 1999 and since 2004-07-01 all cars need to have three point belts on all seats. You can see from this timeline that adoption of the seat belt took its time. It wasn't without opposition.

But the point is: Why are seat belts mandatory? I will get to that indirectly. Lets first look at the problem they are solving.

Between 1960 and 1970, the number of cars on Germany's roads doubled to 14 million, the number of accident victims grew steadily and reached a peak in 1970 with around 21,300 killed. The development of accident statistics alarmed politicians and the population. The public was no longer willing to accept the victims of road traffic without action.

It wasn't only politicians who saw the problem. At least in Germany, public opinion was that reducing death and injury caused by traffic accidents is a good thing.

Is the seat belt effective?

This question might seem irrelevant to the law at first, but it actually isn't. Laws have to weigh consequences, and a law that puts a burden on someone has to have a merit that outweighs the burden.

American, Swedish and British studies have shown that the general use of seat belts can reduce the number of deaths and the number or severity of injuries by 50 to 60 percent.

So yes, seat belts were presumed to be very effective at doing what they are supposed to do, and everything we have learned since then has reinforced this points. Seat belts are probably one of the most effective security tools in a car.

That being said, the German government did not want to make the wearing of seat belts mandatory at that time:

The intention is to refrain from a legal obligation to wear belts, as this would not eliminate the existing prejudices in the population against the use of belts, but perhaps only increase them.

It took until 1973, when accidents rates were still extremely high, that the German government started considering making them mandatory. And while they were made mandatory in 1976, there was no penalty for not wearing them until 1984.

Can you achieve the wanted effect on a voluntary basis?

Remember, it was public opinion that deaths and injuries from traffic accidents were too high. It stands to reason that such an effective tool as the seat belt would see high adoption rates on a voluntary basis, right? No. Humans are funny that way, we aren't rational beings.

A study conducted in the early 70s found that irrational fears which are in no way rooted in reality drove adoption of the belt way down:

The seat belt was primarily associated with the dangers of an accident and its consequences, and only secondarily with his actual function, namely especially to protect against these dangers. For 60 percent, the motorist connected the belt with the fear to be burnt inside a vehicle, for 75 per cent with the Fears that emergency responders could possibly not remove the seat belt fast enough. 40 percent associated the Belt with the idea of bondage. The idea that the belt could, in an accident, cause particular dangers, was latently presents among the motorists, without having experience with it or being able to draw on the experience of others. This was obviously the explanation why fears about the belt stubbornly persisted, although they have been informed about which protective function the belt actually offers for quite some time.

So despite a public want for more safety, voluntary adoption was abysmal due to completely irrational fears surrounding the seat belt. Its a paradoxical situation that can not be solved by making rational arguments and appealing to the individual.

And now, the final question: Given all of the above, is requiring seat belts legal?

And the answer is yes. Weighing the pros and cons, it turns out to be legal, at least under the German constitution:

In simple terms, it can be condensed to the question: May the State force the individual to do something for his own protection? At the introduction of compulsory seat belts in 1976, the German government had explicitly stated that it was of the firm belief that the use of safety belts significantly reduced the number of fatalities and serious injuries that could be.
The fear that safety belts could have a negative effect in certain accident situations, such as a fire in the vehicle or a fall into the water, was unfounded. The Federal Government was of the opinion that the obligation to wear prescribed seat belts did not constitute a constitutionally unlawful encroachment on the general freedom of action. The existing road traffic regulations already restrict the the freedom of the individual in the public interest. The same applies to construction and equipment regulations. Most of the provisions serve not only to protect third parties, but also to protect road users themselves. The obligation to wear seat belts, although mainly for self-protection, would not be confined to that either. After all, the driver of a motor vehicle, who remained conscious because of the protective effect of the seat belt, was still best able to react correctly and quickly according to the circumstances after an accident and thus avert dangers to others. In principle, this also applies to the passenger. In view of this protective effect on life and limb, but also in view of the avoidable consequential costs of the accident for the general public, the public interest in such an effective safety measure was so great that the relatively minor interference with the general freedom of action was justified. This applied all the more so because restrictions of the general freedom of action were in the nature of all road traffic law. In the present case, they were not more severe than in many existing regulations.

And finally, a point on your idea of "freedom":

What I understand by "freedom" is that "I should be able to do anything and everything, if it DOES NOT AT ALL hurt anything or anyone, be it financially, physically, mentally etc."

But traffic accidents hurt people. They hurt the people who are in them. They hurt the first responders. Not being able to render first aid or to call emergency services endangers people. If the seat belts keeps you alive long enough to call emergency services, then a life might be saved. Not being able to do that puts others in danger. The strain you put on the health care system and on social security systems e.g. due to being unable to continue to work is a burden on the society as a whole. Being dislogded from a car seat makes your body a high-speed projectile with the capability to injure and kill other people. Being thrown around in the car makes your body a deadly projectile that can hurt other occupants of the car. The list of consequences to other people and society as a whole is quite long, actually.

Sources

• Deutscher Verkehrssicherheitsrat (Hrsg.): Der Sicherheitsgurt – Lebensretter Nr. 1. (= Schriftenreihe Verkehrssicherheit. 15). 2011.
• Seite „Sicherheitsgurt“. In: Wikipedia, Die freie Enzyklopädie. Bearbeitungsstand: 10. Juni 2020, 15:01 UTC. URL: https://de.wikipedia.org/w/index.php?title=Sicherheitsgurt&oldid=200830049 (Abgerufen: 15. Juli 2020, 08:38 UTC)

What you understand by 'freedom' is not a universally accepted guiding principle.

For example, some lawmakers might be operating on the idea that we should attempt to maximise the health and happiness of society. If you break your spine because you didn't wear a seat-belt, then your health and happiness (and freedom to walk around) is reduced. They then attempt to calculate (probably using a lot of guesswork) whether the average loss of life/happiness as a result of not wearing a seat-belt is greater or smaller than the average loss of happiness as a result of forcing everyone to wear a seat-belt (and presumably having to arrest some people who refuse to do so). This gives us a guide as to whether a law mandating seat-belts will be a net positive for society.

It's a tradeoff between two things: the harm prevented by the law, and the freedom exercised (or harm tolerated) without the law.

While I won't echo the existing answers, I will say that the harm prevented is fairly substantial and potentially lethal to more than just the victim.

In contrast, the freedom infringed upon is tiny:

• Unless your helmet is damaged or misshapen to the point that calling it a helmet stops making sense, it doesn't really impair you at all. It might not feel nice, it might be heavier than you like, or it might come with a monetary cost (which are all reasons not to wear one in normal circumstances), but they're slight enough that calling them impairment overstates them. It doesn't take all that much risk (such as being in a dangerous area, or having sufficiently impaired motor skills) to swing the balance.
• Same for seatbelts; you could say they restrict your mobility while seated in the vehicle, but the only time you're going to be safe enough to exercise that mobility in the first place is going to be when the vehicle is stopped, in which case you can just unbuckle the seatbelt. You could buy a car without seatbelts and save the cost, but who would sell you one, and to whom would you resell it when the time came? And how much would it really save?

Every law that bans something has to consider this ratio, and in this case, the ratio heavily favors the former. There just isn't enough there to infringe upon to justify not preventing the harm.

There are laws that are meant to prevent people from hurting themselves. Examples:

• Prohibition of advertising for cigarettes (or forcing cigarette packs to contain images of lung cancer sufferers, etc)
• Minimum age for driving, drinking, etc
• Minimum age of consent
• Financial literacy tests before people are allowed to buy options in the stock market
• Prescription drugs that require a doctor's note to purchase

There are also good reasons to stop people from hurting themselves. If they are hurt to the point where they need care, then they become a burden to their caregivers, be they their relatives or society as a whole. Even if they outright die, someone still has to deal with their corpse.

You may not approve of these laws, but I suspect most of society do.