My son wants to wear a bra and I don't know what to do!?

My son's 11 and he keeps asking to get to wear a bra. I think he's jealous of his sisters, I have 5 kids and 4 are girls. I'm a single mom, but my alimony allows me to stay home with the kids as a stay at home mom. When my youngest daughter (10) got a training bra a couple weeks ago my son started asking to get one and not a day has gone by that he hasn't asked. When I tell him no he cries and goes and hides in the room he shares with my youngest daughter and refuses to come out for hours (even to the point of skipping meals. I don't know what to do, should I just let him start wearing a bra? I don't want him to turn into a queer little cross dresser, but I don't know what else to do. He's a good kid, quiet, does his chores, gets good grades, etc. He normally doesn't throw tantrums at all. I've tried to explain to him that bras are only for girls but he is having none of it. What should I do?!