Why is going to the prom wrong?
The prom is an occasion for youth to date and to dress up in an unbecoming, unchristian manner trying to get the attention of the opposite sex. Some go to the prom to spend time dancing and drinking while others have other agenda. Many youth commit several sins on that night. I don't think that it is a healthy environment someone should be at even if they do not intend to dance.
Christianity is based on free will and choices, let us make the right choices as St. Paul says, "All things are lawful for me, but not all things are helpful; all things are lawful for me, but not all things edify" (1 Cor 10:23). Therefore "Set your mind on things above, not on things on the earth" (Col 3:2) and "Let all things be done for edification" (1 Cor 14:26).