what is sexuality even

I was wondering really deeply about this, can lesbian/gay/straight people really only like someone for their personality? Cause at the end of the day they're only attracted to the person if they have the genitals of what they like, right? 

It kinda confuses me, because some people who are lesbian/gay/straight say that they do like someone else because of their personality, but they usually bring up a stereotypical argument, be it that men are not emotionally intelligent, theyre manipulative, or that women are too dramatic, things like that. But then that would feed into the idea that "all men/women" are the same, which I dont think is the best!!!

I ask this because I'm trying to figure out the actual workings of sexuality, and the truth of it, cause it doesn't make sense if I consider my personal experience