Why do guys try to prove their masculinity when girls come around?

It's primitive and instinctual—their breeding impulse. Females tend to choose the most robust and appealing male among all mammalian and aviary species in nature. Humans are no different, and males instinctively know this. So they show off for us, and we wear tight clothes and makeup and do our hair for them—because we like them to want us, too.