Because in this sentence is more like someone offering to you come into his house. In this case, the person is asking you to come in because he's already in the house. It depends on the place where this person is standing. If he's outside and offers you to enter before him, it would be 'go'. But if she's inside already the correct term would be 'come'.
Also, Por quê is "why" in the situation where you're inquiring the reason behind something.
E.g. "You're going to jump off the building? Why?"
It is basically saying "For What Reason". Por que(without the circumflex) is for other cases.
E.g " Because I'm going to see if I can fly, that's why!".
P.S this what I have understood from being taught Portuguese, feel free to correct me, just restrain the downvotes please.
There is an article explaning it here: http://educacao.globo.com/telecurso/noticia/2015/01/dicas-do-professor-aprenda-usar-os-tipos-de-porque.html
Entrar can mean to "enter" check http://michaelis.uol.com.br/busca?r=1&f=0&t=1&palavra=entrar