OMG.... so many people believe false information.
Transexuals are not people who "take it all the way" or "want to become female."
Transexuals are BORN transexual. In their brain, the identify as the gender opposite of their physical sex. That means a MTF TS does not identify as a man, they hate everything about PRETENDING to be a man. They are a woman inside. Their internal gender does not match their external sex.
Since you can't change your internal gender, the only thing a transexual can do is change their external sex to match their gender.
A transexual can DECIDE whether or not to transition. They can live the rest of their lives knowing they are transexual, they can suffer quietly in pain and live the way society tells them to live. Many do not do this because they get to a point where they just can't take it anymore and they NEED to transition. For many, it's transition or death.
Just because someone does not transition does not mean they are not transexual... AND just because someone does transition does not mean they are transexual. A man who transitions to 'become' female is still a male. A cross dresser who transitions is still a cross dresser. A transexual who does not transition is still a transexual.