It sounds to me like the Social Skills teacher (Did you mean "Social Studies", which is what we have on this - left - side of the pond) or the kid designated as your "friend" or both had a few social skills deficits of their own. This doesn't mean I don't appreciate the teacher's intentions, though; anyone who reaches out to an Aspie like that deserves a gold star in my book.
In my opinion, saying "Hi, I'm Charlie. Let's be friends..." just doesn't quite work. Instead, he should say something like "Let's go shoot some hoops after school" or "Meet me in the gym for batting practice at 3:00 (or 15:00)" or some other activity that the both of you can take part in, and let the friendship develop on its own from there. And if it doesn't, it doesn't.
Now then, I do feel your pain at not wanting to reject this fella that you apparently have nothing in common with. This might be true if, as an Aspie, you have a feeling of "Who are you to throw friends away?" after being by rejected by too many others for years. I can speak from experience; when I moved to a new town for the start of 8th grade, almost no one talked to me. Years later, one of them confessed that they avoided me because they already had all the friends they needed -- whether that was true or just a smokescreen for the then-unknown Aspie Bug bite, I do not know. But here are some suggestions:
1. Reach out to this guy and suggest a session or two of something you can do together that requires a lot of verbal interaction. Do people your age still play Dungeons and Dragons, or other role-playing games?
2. Invite him along on some activity with your other ("real") friends. Where is it written you can only have two? "The more the merrier" I always say.
If you do this a few times, and there really is no interpersonal chemistry, as you seem to think, he'll get bored and look elsewhere.
Finally, here's one thing I remember learning a long time ago. It seems that in French, there are 3 different words for "Friend" but each is a different degree of friendship. One word might be the guy you share an Algebra book with in class, another word the one you play the occasional Nintendo/Playstation/X-Box game with, and the third one is a super close "Fred-and-Barney", "Laurel-and-Hardy", or "Gilligan-and-the-Skipper" type friendship where you rarely see one without the other. Maybe you can be friends with this guy by the lesser of the three.