You wouldn't understand, you never served in the military

Your friend appears to be linking the necessity of understanding with serving in the military. For this to be reasonable, he or she would have to demonstrate that necessity, or at least argue why the understanding could not arise from empathy outside of the experience. Human empathy is very powerful to the extent that we cannot always tell the difference between an imagined experience and a real one. This might fall under the generic "non sequitur," but rather than call "fallacy", I would seek to better understand why your friend feels this way.