I think that statement is hypocritical. If people felt the need to conform to the stereotypes of a gender, and the only way to do that is to become a different sex, then everyone is still conforming to the old stereotypes and nothing has changed. In that way of thinking, the very fact that a man feels he needs to change his sex because he does womanly things supports the stereotype.
If we want to change things, then it is the stereotypes that we need to denounce, not change the biological sex that someone was born with. We shouldn't call them man or woman based on what it is they do or how they act. Unfortunately, the majority of the population do act as the stereotypes suggest....
So, in my opinion, transgenders are not helping their own cause, they are actually doing it harm, if all they really want to do is change the stereotype. Do you really need to be a girl to act like one? Or is that still an insecurity due to societal norms?
There is no need to mix science and actual fact with the way that people feel inside. If you are trying to make the outside look like how you feel inside, then you are conforming to what society believes you should be.
Bottom line is, you were either born a man or a woman, no one can change that.... and on a rare occasion you can be born both.... like Jamie Lee Curtis.