Poor is often good for expensive private schools like that. You may be in better shape than someone much more well-to-do.
Can you assure him that he can still see his current school friends afterschool and on weekends? (This worked for us with homeschooling.)
If the friendships are all that's bugging him, and if you think it's a better situation than the one he's in, AND if you can get a scholarship for him so that you can afford the school, then it seems like a workable situation. Plus you can always tell him that if it doesn't work out, he could go back to public school. That's one nice thing about public school--they pretty much have to take you. So it's a reversible decision.
I don't think you want to force him to go if he's sure he doesn't want to. But I also think you can confront his fears in a positive and persuasive way.
But I'd find out about the scholarship first. If you can't afford the school, there's no sense in persuading him that he wants to go!
