It could be that people suffering gender dysphoria seek out the military in an attempt to suppress their feelings. Where better to "butch up" than in the military. So this having failed, the person seeks the gender reassignment they were fearing for so long.
It could also be that the military life and its overtly male culture contrasted with the current US zeitgeist leads to seeking to abandon male gender in protest against that culture. What is the most "anti-military" action? How about abandoning manhood in favor of womanhood? And one could see female to male reassignment in the same light; joining behavior rather than protesting. My suspicion is that the overwhelming majority of these GID cases are male to female.
Then there is the possibility that the male soldier, traumatized by the stresses of combat (or even just military life) escapes in the most irrevocable way ever.
I have another thought about male to female adult gender reassignment. Could it be that the person transitioning rejects homosexuality and finds transgenderism a way to have sex with men without being "gay".
I am deeply skeptical of childhood gender reassingment. Even of the diagnosis at at all. I am also skeptical of adult transgenderism. Or at least the relative ease with which we allow this odd behavior.
From an epidemiological standpoint, the highly technical explanation for my concerns goes something like this: There is something rotten in Denmark and it ain't the fish".
Ronald Reagan was surrounded by Secret Service agents when he was shot. If he had an armed math teacher?
We go high. They lock up children in cages.