Seriously - nobody answered PP's question. What the [bleep] is a cotillion?
If it's so good for boys, why don't more do it? Sounds creepy that they have to recruit sweaty palmed boys - blech.
How do Cotillion parents justify spending $400 to meet "new" (as in marrying/breeding stock?) when they could send that to cyclone/famine relief?
If it's fun and kids like it, maybe someone could set up a charity version where kids dance AND raise money for less superficial causes? How about "Baby Loves Ballroom"?
At G'town U we had "service" fraternities that kind of combined the best of a frat (group parties

) with something you could actually put on your resume (helped homeless). It was a funny kind of "faux" exclusivity that helped make sure we didn't take ourselves too seriously.
I've outsourced etiquette to my MIL.