Clinical Psychologist, Psychologist
The short answer to this question is that veterans are highly likely to be placed and have experienced highly stressful situations where they may at times be sleep deprived, fearful of their lives, running into danger when someone else would instinctively run he other way and so on: In short they experience significant levels of anxiety in their work. This predisposes them (there is a great Australian documentary called “You're not in the Forces Now” done by Vietnm vets that explains this) to anxiety disorders when they are outside the military - ie in civilian life. Anxiety and depression go hand in hand, it is rare to have one without some of the other. Coping behaviours such as alcohol consumption, bottling up emotions etc also contribute to depressive symptoms.
I get the feeling that the question you have asked is in fact a very simplified one of a more important question you have. I would encourage you to share that either here or with a mental health professional who is comfortable working with Vets or their families.
I hope that I have provided enough of an answer for you
All the best
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