“What if my child both hates school and likes being in school with all his friends?”
If he is not happy with either option, then there is a lot more for you to do than just leaving him alone to make the choice. Him being in control of the outcome is merely a necessary, not a sufficient condition.
There is a possible life style for him that he can enjoy and feel good about embarking upon. If that life style is neither captured by the phrase “staying on at school” nor by the phrase “leaving school”, that means there is a problem to be solved here.
There is a reason or reasons he finds each of these suggested outcomes unpleasant. Therefore, to solve the problem, it is necessary to discover what he wants to get and what he wants to avoid. Then you and he have to think of ideas for how, with your help, he can get what he wants to get, and avoid what he wants to avoid. (I don’t mean in the long run, I mean while enacting the decision that you all come to.)
You should expect “what he wants” (and what you want) to change, perhaps radically, during the course of this problem-solving process. The object of the exercise is not to find good things that outweigh the bad ones, but to find an option that he can exercise without any internal conflict – an option which, when he exercises it, will not cause him to yearn for any of the rival options.
From the perspective of taking children seriously this seems like one of the more trivial problems to solve. His reason for wanting to go to school is probably that he likes spending time with his friends. So surely it is very easy to meet that wish without him having to suffer years of torture at school? Even school children get some time off in the evenings and at weekends and in the holidays.
How about actively creating get-togethers outside school hours, that his friends will find appealing, and that will meet your son’s wish not to become a (mythical!) unschooling autodidact devoid of friends? How about making a point of joining the many home-educators’ get-togethers, where your child will meet other children who do not go to school? Many such individuals are extremely interesting, precisely because their thinking had not been channelled into the narrow confines of acceptable thought in the authoritarian institution that is the school system.
Or perhaps it is not the usual wanting to spend time with friends reason. Perhaps her heart is set on a career in chemical engineering and you do not have the equipment and the chemicals she needs to pursue her passion. If you are unable to provide that for her, is there a graduate student in Chemistry or Chemical Engineering who would be delighted to meet a child who shares the same passion, and who would love to show her stuff and teach her whatever she wants to know, and so on? Often, people who are passionate about their field are delighted to meet children who share their passion, and they are far more generous with their time than any of my school teachers were.
The point is, there will be something good that your child wants, and something bad that your child wants to avoid. We just need to find out what those things are, and start thinking laterally to come up with a solution that provides the good and not the bad.
Sarah Fitz-Claridge, Taking Children Seriously FAQ: ‘What if my child both hates school and likes being in school with all his friends?’, https://www.takingchildrenseriously.com/what-if-my-child-both-hates-school-and-likes-being-in-school-with-all-his-friends/