And that's perfectly acceptable. I don't expect that inviting my son somewhere means they should invite me too. Just because your kids are friends doesn't mean the parents also have to be.
My son likes lots of alone-time too. But sometimes he wants to meet up with a friend, like on a weekend or something, even if just for an hour or two. It's up to the parents to facilitate get-togethers if the kids want to play outside of school. When I was a kid we did this sort of thing all the time. My parents would invite my friend somewhere with us, then I'd get invited somewhere with them, etc. I guess I'm just surprised that parents don't seem to do this anymore. My son has expressed an interest in playing with some of his friends outside of school. But unless we make the effort to make this happen, it wouldn't happen at all. My neighbor is the only person who occasionally calls up and wants to know if my son can come over to play. Maybe kids are too involved with other activities to do this much anymore? I guess I did assume that if I invited someone's son to do something with mine, then at some point, the parents would take their turn at doing the inviting, even it was just once a while.