Lol...not the type of rivalry you envisaged, but when I was a lot younger, I used to be upset whenever another handsome guy joined my class 'cos in my mind everything was a competition. I just wouldn't talk to the new handsome guy, no matter what. Anytime I look back, I can't help but laugh at my foolishness. I'm still competitive; but just not when it comes to trivial things like physical appearance.
Did you have a rival in school? Let's hear it.