How can I get my parents to see that social interaction is irrational, and I should be left alone?

That's not very logical at all. On our planet, even if you are the smartest person on it, if you sit in a closet ad don't speak to people, then how will you advance the world? You won't. If you ever want to do anything, you need to learn how to socialize, and that starts in high school. You don't necessarily need a girlfriend, but you do need to have some friends and have some normal fun (like dancing) so you can learn to socialize. Since you've been home-schooled for so long, it sounds like you're trying to make this logical because you aren't good at it. But unfortunately, it's a very valuable skill, which you really need to develop in order to advance the world at all.