If options gives you the RIGHT but not the OBLIGATION to exercise them, then why are they being forcefully exercised if they expired in the money?

Options are automatically exercised after expiration because there is someone that is expecting that specific result.

When you buy an option, there is someone that sold an option. And vice versa.

The assumption is that someone is waiting to be delivered shares. Both parties are responsible and it is worse for the brokers to assume that one is irresponsible. Because, as options are actively traded, the brokers cannot chase people around to ask if they wanted shares or not, all the options were sent to a pool of fungible assets and they need to be quickly matched up with shares and closed out.

Maybe an emergency came up, and you weren't able to access internet for a while. Maybe you got into an accident and were in the hospital for some time. Whatever the reason, you weren't able to access your online broker during those time.

Suppose you bought some shares at $1.00 each, hoping/expecting them to rise in value. Shortly after, an emergency/accident hospitalised you. During that time, the shares did indeed rise to $1.50, but being in hospital you were unable to realize your profit. Unfortunately, by the time you left hospital and were able to contact your broker, the shares had dropped to $0.50.

There's not a lot of difference between what you're asking about and expecting your broker to have automatically sold the shares when they were at $1.50.

Essentially, there are four¹ things that you can do when call options approach/reach expiry:

1. Let the call options lapse. You choose not to exercise your right to buy the underlying shares.

2. Before expiry, sell the call options to someone else who then owns the right to purchase the underlying shares.

3. Exercise the call options and immediately sell the underlying shares you (briefly) acquire.

4. Exercise the call options and acquire the underlying shares, which you keep (at least for the time being).

In the absence of instructions from you, what should a broker do? From their point-of-view, (1) would be the simplest (essentially, "do nothing"), but I doubt anyone would be happy with that choice if the options expire in-the-money. One problem with them choosing option (2) or (3) is that you might have originally bought the options with the intent to hold the underlying shares (plus, with option (2) they would have to do "extra work" to find a buyer).

Overall, it seems to me that option (4) – exercise an ITM option and retain the underlying shares – is the natural "default choice" for the broker to make: it's the simplest for them (other than letting the options lapse) and doesn't try to "second guess" why you bought the options in the first place.

According to Question 11.3.5.5: Will my broker automatically exercise options that expire in-the-money? of the The Options Industry Council FAQ:

Each brokerage firm has a procedure outlined in your account agreement forms. Customers should be familiar with these procedures. The option holder can always submit instructions to their broker regarding whether to exercise or not to exercise.

This suggests (though I have no experience of trying) that if you are unhappy with your broker choosing option (4), you may be able to submit instructions to them to pick another option.

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¹ As Bob Baerker correctly pointed out, the distinction between (3) and (4) (whether or not to hold the shares acquired) is not part of "the option process", but a separate investment choice. However, the overall result of those two separate choices does give four outcomes.

Regarding automatic exercise, brokers do not automatically exercise the options. In the US, if an option is one cent or more in-the-money (ITM) at expiration, the Option Clearing Corp (OCC) will automatically exercise options whether they are long or short. This is called Exercise by Exception. For equity options, you will end up with a long or short position in the underlying (index options are cash settled).

If you are long the option, you can designate to the OCC via your broker that it is not auto exercised at expiration. This would make sense if it is ITM by pennies and your commission and/or fees to close the position exceeds the ITM amount.

Per Investopedia:

Automatic exercise is a procedure implemented to protect an option holder where the Option Clearing Corporation (OCC) will automatically exercise an "in the money" option for the holder, typically at an option's expiration date and time.

Regarding your concerns about being unable to access your account:

Maybe an emergency came up, and you weren't able to access internet for a while. Maybe you got into an accident and were in the hospital for some time. Whatever the reason, you weren't able to access your online broker during those time.

Suppose you bought 1,000 shares of AAPL on Wednesday for $127 and later that day you were in a car accident and needed surgery. Is it your broker's responsibility to determine at what price you should sell your shares for a tidy profit? I think that you know the answer to that. NO. It is your responsibility to manage your positions and if you were concerned about the risk, you could place a stop limit order to limit the loss as well as a trailing stop to lock in profit. Such orders could be adjusted every day.

I know first hand what's involved here. In early November I had nearly 200 long and short options in my trading account for various near term weekly expirations. These were mostly long and short collars hedging some sizable positions in 9 large cap stocks.

Shortly thereafter I contracted a bad case of Covid. After two weeks, I reached respiratory distress. I went to the emergency room fully expecting to be hospitalized. Before I went, I spent a morning closing out all of my positions because of the potential risk of an inability to continue to manage my positions if I got worse (my protective options would expire and I would then have full directional risk). I was about as sick as one could get without needing hospitalization (a silver lining?). So, been there, done that and my advice to you is to work out a contingency plan in advance for possibly being indisposed.

You have a right but not a duty to vote in the 2020 presidential election. That doesn't mean you can exercise that right on November 4th. Inaction is still an action, exercised by your choice alone.

Don't you agree to the terms when you buy your options? When you open an account with your broker?

Imagine your question being asked in any other economic dynamic:

I had every intent to return my VHS tape to Blockbuster on time, but a broken down car prevented me from doing so. I shouldn't have to suffer the fine.

Kind of sounds stupid when put that way, doesn't it? Its all about personal responsibility. And, dare I say, the inherent risks in the market you choose to operate in. We all occasionally regret buying too soon or too late, selling too soon or too late. It goes with the territory.

Someone has to suffer the loss, don't they? Someone has to eat the difference. Why not the person who chose to take on the risk? Who else?

You're essentially complaining about consequences when two aspects of your personal life, poorly coordinated by you, collide and have undesirable results. Ad hoc rationalizations and hindsight-bias, posterior risk aversion isn't a get-out-of-jail-free card, despite what leftist academia tells you.

Those are my genuine thoughts on your "hypothetical" scenario.

Options are not forcibly exercised when they expire in the money. If you own an option, and you don't want your broker to exercise it even if it expires your money, you can instruct your broker not to.

Source: The Options Industry Council FAQ, Options Exercise, question 11.3.5.5:

The option holder can always submit instructions to their broker regarding whether to exercise or not to exercise. A customer may decide not to exercise an in-the-money option in some cases.