Children need recovery time, and space, and peace, if they've been schooled, before their curiosity and joy can return.
If school had broken his leg, you wouldn't keep pushing him to do stuff that made it hurt until it had healed and you wouldn't push him to do stuff that was different but similar—basketball instead of the football that caused the break. See the harm to his self-confidence and ability to live joyfully the same way. He needs time and space to heal in whatever way works best for him.
Making a safe nest for him at home, free from any comparison or criticism (implied, inferred or overt) is what he needs you to do right now. Make his nest as safe as possible for him. Make sure he knows for certain that you're not going to judge him or try to persuade him out of his nest before he's ready. Make sure he knows for certain that you feel positive about his need for his nest time, not fearful and anxious. Make his nest feel as safe as you possibly can and, while he's healing, bring the sparkly to him. And make sure it's things he finds sparkly or you genuinely believe he might find sparkly if he eas aware of them and *not* stuff you think he ought to find sparkly or ought to engage in even if he doesn't.
Focus on healing any part of your relationship that has been damaged by schooling as well. Look up Maslow's hierarchy of needs and remind yourself that your job as an unschooling parent is to make sure the lower levels of need are met to enable the higher ones to be possible - safety and security, food, sleep, relationships. And seek to create joy from what he's able to do right now.
Focus your energies on those priorities and watch him and you will begin to see signs of healing; you'll begin to learn who he really is without the influence of schooling and all that entails.
If you do this healing time badly—forcing him to do things before he is ready to or when he has no interest, judging and fearing his need for a healing nest (you wouldn't fear a plaster cast and time not playing football and etc. if he'd broken a leg), the healing won't happen and you're unlikely to see the return of joy and self-confidence you're hoping unschooling will lead to. If you do this healing time well, you will see him flourish; you will see your relationship strengthen and you will begin to really know your son and what makes him tick and you will get better and better at responding to who he really is.
"Look up Maslow's hierarchy of needs..."
click for an explanation if you want one
So if he went to 5th grade and maybe kindergarten and possibly another preschool year or two.... It will take him between six and eight months to recover. And summer didn't count. Six to eight months starting when school started. And every time the parents get schooly, that six+ months starts over.
I'm serious about this, and there are no shortcuts.
Meanwhile, the parents will need to be deschooling for over a year.
Parents shouldn't rush it, they should relax into it.
Read a little...
-=-he doesn't want to go out of the house, he doesn't want to meet with other children or participate in any fun activities with other kids-=-"Fun" isn't fun if he doesn't want to do the thing. Don't think of something as a "fun activity." It could be torture. So if he's rejecting torture but you're calling it fun, that won't help your understanding of him, or your relationship with him or his trust in you.
-=- even protested about going to a homeschool gym class.-=-Sounds like you went anyway. See the paragraph above.
If he's been harmed by comparisons to other kids, let him avoid other kids for as long as he wants to.
~ Getting him out and even if he sits in be corner other kids will come up to him and eventually he will open up. ~Not necessarily. If part of the problem at school was too many people "coming up to him" (and that can really be an issue for introverted kids in school, where they have no choice but to be with other people), then putting him in a situation that mirrors that experience would be a setback.
~ eventually he will open up ~Again, not necessarily. A person who needs plenty of alone time will not respond by "opening up." It might look more like finding another corner where people won't bother him.
I say this as an introverted parent with an introverted child, and in the past, I have gotten that wrong, hoping more socializing would "help." It never, ever did. Especially forced socializing or staying longer than she wanted, even at someplace she wanted to be initially.
If a parent is the opposite of the child (extrovert/introvert and vice versa), it can be tempting to do what make *you* feel comfortable. (And by extrovert, I mean someone who tends to get their energy from being around other people. An introvert gets their energy renewed by being alone.) So extroverted parents might want to get out and do stuff! With other people! Introverted parents might want to stay home and read or watch a favorite show or surf the 'net. Meanwhile, their kid wants just the opposite.
Unschoolers here have said this before (and this is especially important for children who are deschooling and their parents): look at what makes your kid happy, what fills their cup. What they, as individuals need. Give them more of that, find possibilities for them that connect to that, allow them to say yes or no with no strings. It is part of forming that bond of trust between parent and child, so that they believe you have *their* best interest at heart.
Another introverted parent of an introverted child here, and I can't 'like' that comment ^^ by Robin enough.