That's because "Support our troops" has never been about supporting the actual humans in the military--it's always been about supporting the wars those troops are fed into and the administrations that wage them.

To be generous, some of it might also come from memories of shitty treatment of returning soldiers in the Vietnam era. But for all of my adult life, it has just been a rebuttal to people expressing anti-war sentiment. The exact same way that "Back the Blue" is a rebuttal to people protesting police violence.