As Frances says there no such thing as late onset transsexuality. You are either born with this condition or you are not. Depending on the intensity of your condition you may transition earlier or later. To me the distinction between a 25 year old and 50 year old transitioning is completely artificial. Once you have completed puberty it really does not matter anymore. If you are transsexed then you will transition.
I do not think that TS really experience such a thing as being born into the wrong body. Your body is defective, genetically, organically and physiologically. This defect must be corrected.
You cannot become a woman you either are one or you are not. Being a woman with a defective body comes with social consequences that start at birth. Being socialized according to your genitals is one of them. Once you are socialized as a man, the process is not one of "becoming a woman" but rather to remove and ameliorate the effects of being socialized as a man. That is the hard part.
I don't much subscribe to the suppression, repression and depression theory per se. I do however believe that the transsexed sometimes refuse to cultivate who they are for fear of social reprisals and often begin to cultivate a maleness as if they had something to prove to themselves and the world in which they live. Depending on how intense their condition is this may take years to overcome.