Trump managed to avoid military service during the Vietnam era by a fairly spurious (pun intended) medical deferment. He has spent his entire adult life, until now, making money by screwing people over. He ran for president because he saw the presidency as a prize, not a sacred trust. He uses his office to expand his ego, not to help people. In short, he has no concept of public service whatsoever.
He has, however, surrounded himself with military men to whom service presumably means everything, and they defend him. Hence, the paradox.
There are very real dangers here. The military consists disproportionately of people from red states and minorities. If the connection between Trump and the military causes people in both parties to see the armed forces as just another wing of the GOP, much like evangelical churches, the implications for a divided country will become very serious. Blue America will become alienated from the people protecting them, the red portion of the military may consider blue people not worth defending, and the military itself may split politically between its red state and minority components.