Imagine for a moment that you live in a country that has fought a half dozen wars somewhere in the past century, and that every one of those was (more or less) morally justified. Your great-grandfathers, grandfathers, and father were probably drafted into those, fought and (likely, you were born after all) returned.
But the next war comes up, and everyone tells you that it's righteous too. Maybe they're mistaken or deluded. The people in charge, demanding this war, they aren't supervillains either. They believe they're fighting communism, and while they probably couldn't have known for sure at the time, history has shown it to have been horrible enough that some sort of strategy should've been employed (even if not a shooting war).
Are you going to be the one to back down? There's none of this wokeness that exists today. You'd be called worse than just a pussy for dodging it. Even those who knew of and understood shell shock only cut slack for those who had suffered it, you wouldn't get pre-emptive sympathy.
And those grandfathers and fathers who did go off and fight, you're sort of insulting them though not coming out and saying it outright. If you're morally justified in dodging the draft, should they have done the same? They didn't, so are they just amoral killers now? And this isn't going on in your own head, not entirely, you can tell they're sitting there thinking the same thing, wondering if you'll be one of the hippies that insults them by dodging.
There may be moral principles strong enough that it would demand someone dodge the draft, but those sorts of principles aren't popular or encouraged in the US. Why, if people will dodge the draft during bad wars because of this, what does it mean if the principles say "all wars in which enemies aren't landing on our beaching and dropping shells on our undefended cities are bad"? Well, it means that officeholders who will eventually want a war of their own can't have it. And all officeholders eventually want a war, even if they all can't agree on which.
That's why everyone didn't dodge the draft. Sociological pressures, psychological pressures. Ambiguous popular moralities and people not wise or strong enough to create better ones.