Actually, they do.
Males are given estradiol and antiandrogens to reduce prostate swelling, and certain types of prostate cancer.
In nearly all cases the male body feminizes as would be expected from what we MTF's refer to as HRT. However, the males who receive this treatment, who have not been diagnosed as transsexual, regularly feel depressed, sad, and angry from the loss of their manhood. The depression can become quite severe and require anti-depressants in addition to the cross hormone therapy.
The do not become calm, they become quite agitated. They do not feel more feminine, they feel that they have been deprived. Conversely, trans women often times become more calm and serene.
It is not conclusive proof of being trans, but it is statistically significant.
Unfortunately, there is no common cross hormone therapy for women that has any clinical basis, so it is difficult to say if this would be true for trans men.
-Sandy