Choosing to be a homosexual means, choosing to have attraction to the same gender, and that's not something that people choose. Homosexuality is called SEXUAL AND EMOTIONAL ATTRACTION TO THE PEOPLE OF THE SAME GENDER (try to understand the definition well)
And yeah, people do CHOOSE to come out of the closet, fight for rights and everything, but why is that? That's because everyone deserves to be with who they love. Straight people gets to be with the person they love, so why not homosexuals?
They choose to come out of the closet, because there is no mark on our body, which represents that a person is gay/bi or anything. If there was a mark, we wouldn't have to come out. We wouldn't have to tell people, because they will already know. Heterosexuality is DEFAULT. So, at first, people will just think that a person is straight, so the gays have to tell people that they are gay. Imagine a girl falling in love with a gay guy. If the girl never knew that he was gay, the girl would be chasing him, so it is necessary for him to tell her that he is gay. If the girl and the gay guy gets into a relationship, the gay guy wouldn't truly love that girl.
Letting others know that they are gay, saves the opposite gender from getting heart broken (if they ever fall in love with a gay person)
Before people come out of the closet, they're still gay. They just hide the fact that they are gay. Why is it so hard for people to say it? It's because there are people who will hate them after they find out that the person is gay. Sometimes, it could be a huge turn around in a person's life, to tell someone that he/she is gay.