This post is in response to another thread where posters wanted to discuss this, but didn't want to derail the thread. So I said I would start the thread here.
A basic element of feminism is that women and men are born as that sex - biologically men/women, but society socialises us to behave as our alloted gender. Gender is the idea that women and men behave in certain ways. And we are all socialised in this even if we reject it or try to as adults.
For example, research shows that people treat the same babies differently depending on whether they are told they are boys or girls. The media pumps images to our DCs about what a girl or a boy should be interested in, play with and wear. Teachers are more likely to allow boys to speak out to the whole class than girls - well researched.
Feminism challenges these gender constructs and says that girls and boys can enjoy doing the same things, etc. Transexuals talk about being born in the wrong body e.g. born in a male body, but feeling like they are really a girl/woman.
But this is obviously at odds with feminism. Sex is a biological fact. You are born in a male or female body. Behaving or feeling like a man/woman is supposed to feel, is an artificial construct. Because what does a man or woman feel like? We only feel like ourselves as individuals. So any idea of feeling a man or a woman or a boy or a girl is based on an artifacial idea of how a boy/girl is supposed to feel.
So the basic idea of being born in the wrong body, is contradictory to the basic ideas of feminism.