Quoting Laverne Cox

[…]

I've been saying this for years, that gender identity and sexual orientation are different but so many people don't know. I think that the reason for that is that we are in the LGBT community and we get lumped with gay and lesbian folks and bisexual folks, but [for us] it's not about sexual orientation, but gender identity. I also think that a lot of the issues that folks seem to have with gays and lesbians, particularly when kids are bullied, are about gender. It's about someone assigned male at birth not acting the way a boy should act. So much of it comes down to gender and this fear of femininity in our culture. Julia Serano talks about this so brilliantly, even in the history of feminist theory, femininity has been presented as something that's artificial and masculinity is something that's authentic, and even in a lot of feminist discourse until recently, femininity was seen as something that was artificial and fake. So there is this fear of feminine that we see in a lot of different aspects of culture that is punished. That's a part of patriarchy. In a lot of ways we can't talk about homophobia and transphobia, without talking about patriarchy. 

Source: Gawker - “I'm Good with Myself”: A Conversation with Laverne Cox.