Here's my two cents for Incog and Grin:
I vote for doing what your kids are asking for, but perhaps with a little negotiating to make sure you get what you want, too. I really think that learning to manage social relationships is as essential a part of growing up as academics. In fact, as adults, more people are successful and happy because of their social skills than their academic skills (that's my experience, at least). Your kids are telling you very clearly what they want, and feel that they need, socially. It seems to me that their arguments are well-founded. Even if it doesn't turn out well, they will benefit from the opportunity to try it and see. We learn from both mistakes and successes. And having our parents honor our perceptions and experiences is valuable.
If the worry is that their academics are going to suffer, then come up with a plan to make sure that they get academic challenge somewhere else. You can even say, OK, we'll do it your way, but what are you willing to do outside of class to make sure you are continuing to learn? Maybe a language, an academic contest, working independently on a project... It seems like a fair trade and my guess is that the kids will jump at it. They like to learn, after all.
