How to instill scepticism towards authority, albeit in a healthy way?

Further to your own and @candied_orange's point as well, your son's first teachers of authority are his parents. In fact I would argue that a person's primal mental/emotional interface with authority is birthed and given dimensions within their nervous system right here.

Each "no!" issued by a child's parents lays a subtle layer of acceptance of authority when that child engages with a wider community.

If the "no!"s are enforced with use of threats or other intimidation, this too lays another much more complicated kind of relationship with authority in the child's awareness.

(And the "terrible twos" might better be understood as an outcome of "ignorant parenting").

If one's desire is to nurture a healthy skepticism of authority in one's children, then their skepticism of "overreach" of parental authority itself ought to be nurtured and rewarded always, ideally without fail, ideally from the outset.

To answer the last part of your question, you might lift the ante in some ways, diversify the situations, risks, intensities of experiences that challenge the boundaries of self-assuredness. Either through shared activities like team sports, or other independent actives like hiking or rock climbing, or anything else that introduces more stresses and challenges to the nervous system.

I also want to suggest a book.

The Emperor's New Clothes by H. C. Andersen.

It should be easy to find an illustrated version appropriate for a 9-year old.

Never say, "because I told you so".

When every rule comes with a why the world makes sense. When "because I said so" is the only explanation, authority is the only reason.

Now this may lead to your kid standing in the middle of the street asking "why" when you tell them to get out of it. But if they live they'll have a healthy questioning attitude towards authority.

I find the most important part of a healthy skepticism is in dealing with situations where there isn't a right answer. In the case of puzzles, your son is either right or they are wrong. There is a truth-value that can be assigned to the phrase "I am right." In this case, the person who is arguing for the right side will always win. It doesn't matter if they are the authority or the subject. Right is right.

There are, however, many situations where rightness is more nebulous. This is where "emotional maturity" often comes in. This is where the concept of respecting authority really comes in. When one acknowledges that there may not be a right answer, and defers to authority, a very different skillset comes into play. There is a maturity which lets one recognize what the authority wants, and how to work with it instead of fight it.

I find role playing games are more effective for this than puzzles. Find something both of you enjoy where there is an authoritative figure and a subservient figure. Do that thing many times, swapping roles. Over time you should be able to demonstrate what you believe a good authority figure is like, and you can demonstrate how you believe one should act under an authority. For example, "you shouldn't hurt people" is a phrase which an authority figure can state with many different tones of voice. Each one comes with an implication about how the authority figure sees the world.

I believe the key to such an approach is to keep it a game. Even if there is opposition in the game, at all times you should be supportive of your child, and be ready to end the game on a moment's notice, with perhaps nothing more than a lesson learned. Hold onto that power. And, one day, your son will realize how important that power is because they will be engaging in something that is not a game. And then they will have appreciated the practice.

There is a great book by George Orwell called "Animal Farm", I believe I read it around your son's age; I may not have picked up on all the symbolism on the first time through, but after reading it multiple times I can say it shaped my skepticism towards politicians and other figures.

There are multiple times in the books where certain animals use lies, propaganda and outright force to rule over others.

Note: While I believe this book is mostly age appropriate (Sure some Animals die which is sad) Orwell's other great work in this vein, 1984 is decidedly not child friendly.

His essay on shooting an elephant is also a good look into how authorities and populations act.

How to instill scepticism towards authority, albeit in a healthy way?

In order to simplify the process, we have a natural mechanism for scepticism towards authority. It is called "puberty" and generally happens by itself - as healthy as one manages.

Since your son is 9y old, in 3 or 4 years you will be generally dealing with the opposite problem.

The lesson you're trying to teach is political, and I'd say at a rather complex level. If you wish to pass on a certain political view with regards to authorities, I think that is too complex to infer by modelling societal structures within your family. Such a model would be too crude to be able to cover the nuances of when respecting authority is vs isn't a good idea. Shouldering the role of the authority figure to be disrespected yourself will, I think, not teach this specific lesson. This is better taught by direct instruction. A nine year old is certainly old enough for basic discussions of right and wrong at a societal level; how society is built and what power dynamics is at work.

So share your view. There are countless real world examples of people disobeying authorities, both good and poor. Explain why you think some are justified in what they're doing, and others not. Discuss the ins and outs of breaking quarantine rules to protest against systemic oppression. That issue has an appealing number of layers, for the sake of discussion. Large gatherings inherently a health risk, so that's obviously bad. But then there are doctors who come out in support of the protests, saying racism is even deadlier than the virus. Are appropriate steps to avoid infection taken? Are they sticking to their cause or using it as an excuse to riot? How does their gathering compare to the police spraying tear gas inducing coughing, presumably worsening the health hazard?

To the extent that I interpret correctly what you're going for, I think just teaching that authorities shouldn't always be respected is a proximate goal, where the ultimate goal would be to find the guiding principle for whether or not to respect them in a given instance. I think you should teach the latter, rather than the former, to minimise the risk that the lessons are applied naively and inappropriately.

The guiding principle I might attempt to teach is that we collectively write the laws. At first glance, it may seem like they rule over us, when in fact we have the power to change the laws. Laws are attempting to create a just society. If the laws turn out to be unjust, then that law is dysfunctional and should be fixed. Laws can never tell us what is morally right. We decide what's right, and then write laws to approximate that. And that is a perpetually ongoing process. Likewise, the power politicians have over our lives is not handed down from above, but up from below; they're only exercising the power we've collectively delegated to them.

I believe civil disobedience is an absolutely critical component in the checks and balances that make democracy work. But those are my principles. Yours may be different, but you get the idea. Teach the higher order of rules so that your child has at least the framework to think about whether a specific resulting policy or action is justifiable.

I think it is helpful to give a child this greater picture, but in practice, there are important caveats. First, you need to also bring up the notion that your child might not have access to all the aspects of an issue in order to critically evaluate whether it is just. Second, I think it is helpful to distinguish between what's justifiable and what's advisable. I personally am not putting myself in harms way for every injustice in the world. While a person like Gandhi may be a role model to most of us, we may still not be willing to put up with the amount of jail time and hunger strikes he was able to endure in order to effect change. We must teach the risks, but I don't think that should make us lose sight of what's right.

Skepticism is a disbelief in something or someone. Therefore it isn't a quality you should or can teach. Skepticism of one thing only arises when an alternate path emerges that is obviously better. For instance, sheltered children often have no idea that there are any other ways of life than their parents' until they reach teenage years. If a child grows skeptical about something, it is only because something else has been introduced.

The challenge is to introduce ideas and modes of being that are strong/good enough to make children skeptical of behaviors and situations that are destructive. I should think that humility is one of the core virtues that would allow a child to have the appropriate level of openness while allowing them to be skeptical of harmful situations.

I think the word you are looking for is "critical thinking", which I define as the inclination to always question statements of fact or authority. This is more than just mechanical contraryness, which I observe is a common substitute - critical thinking means that you always check things to your own satisfaction. A sometimes annoying (for others) consequence is that you keep asking questions, sometimes inconvenient questions, sometimes questions that others think are "stupid". To be a genuine, critical thinker, you have to always be willing to abandon your opinion, if facts show you to be wrong. This is, by the way, also at the core of sound, scientific thinking.

In my experience it can be quite a long process, teaching this to children. You at the very beginning by showing that asking questions is always allowed without exception, and that questions deserve an answer; sometimes (quite often, I imagine) the answer will be "I don't know, but you/we can try to find out ..." - this will teach several things: like, finding the truth is often a process, and nobody knows everything. Especially the people who are too certain in their opinions.

I think you are doing very well already; as for why moral rules are right, think about how they function in a social group: we humans are social animals, and depend on others in our group - it is necessary for the individual, that the group survives, and it is necessary for the group that every member can trust on the other members. If you are religiously inclined, you may introduce God around here, but I've never seen the need; group dynamics explain moral values.

Finally, you will never get to the end of the questions - that is the beauty of it, in my opinion. There is always more to discover - there is no final truth.

"Healthy disrespect" for authority has a wide definition. Based on your question, I'm going to define it as "not accepting blindly what authority figures tell him, but not doing it in a way that explicitly defies the authority in a confrontational way". Basically, not automatically trusting authority figures, but not being a jerk about it.

First - I'm not sure it's a great idea to lie to encourage this. He'll figure out what you're doing, and that'll backfire on you. What you're doing seems like one good approach, though; just modify it from lying to him, to asking him to prove his statement, and asking "What about..." things that turn out to be wrong/irrelevant but make him question his approach. That's really the same thing, just without the lying. Lying to him is only going to make him distrust you, not authority figures in general - authority figures are very different from parental figures, in important ways: parental figures are much more inherently trusted as "safe", generally.

Learning to think analytically is the key here, though: and that's exactly what you're teaching him to do by questioning his answers. Not taking anything as given, but considering its source and its veracity. Push back on statements-of-truth from him, and he'll learn to do the same to you and other authority figures.

I have a child in roughly the same category - pretty similar level of math skills, almost same age. I have I suspect the opposite problem: helping him learn to respect authority figures in a way that is appropriate. He automatically disrespects authority figures, as he's confident he knows better than they do (myself included, for the most part). That's a big challenge with some gifted children: convincing them that sometimes other people do know more than they do.

For him, I try to talk through why people are doing what they're doing, and help him to think through their possible reasoning. This should be effective for children on both sides of the issue here; understanding why someone else says and does what they do is important for developing empathy, and for accepting why people might do things that are not what the child would prefer (assign homework, have a pop quiz, ask them to sit down, call on other children...)

Learning how to recognize someone who has a position of authority for a good reason is important, from both sides of this. A person should learn to take different inputs to determine how much respect is appropriate for a person: start with a position based on their authority level plus an uncertainty level, then lower that uncertainty level as they learn more about them and adjust the position accordingly. It's just like a statistical problem: define your prior, then test it using Bayesian inference.

Person: Calculus teacher. Prior: Likely knows math well given position.

First month, teacher effectively explains L'Hôpital's rule, seems to go into depth. Adjust respect up some, adjust uncertainty down.

Second month, teacher incorrectly grades problem set, acknowledges issue and corrects. Adjust respect up some (but be more careful with grading), adjust uncertainty down

Etc. ... and maybe the opposite if the teacher is not so good! If your child is able to understand this kind of thinking, then perhaps this is an effective approach to explain to him.

Finally - modelling is the most important thing I think you can do at this age. Model both how to correctly question authority figures, and how to give deference when it's appropriate. Talk about it afterwards if it seems particularly interesting.