As far as the Draft Dodger label goes, many young men opposed the Vietnam war, with good reason. Many were war resisters, more than they were draft dodgers.
If you want to hold all who avoided the Vietnam War up as cowards, you need to include Geo W. Bush, Bill Clinton, Newt Gingrich, Dick Cheney, Mitt Romney, Pete Seeger, Muhammed Ali, etc.
During the years when the draft was in effect, you could legally avoid being drafted by volunteering for any branch of the military, including those that (back then) had little chance of ever seeing combat. That included the reserve component of all branches, plus the National Guard and Air National Guard units of every state, plus the Coast Guard.
Thousands went to Canada and were eventually pardoned, because it turned out the entire war was immoral and unjustified and no one would argue any longer with any man's desire to resist fighting in Vietnam.
My uncle was a Lt Col jet fighter pilot in Nam in the USMC when I turned 16 during the Vietnam war, and once told me if I got drafted to go to Canada. When I asked how he could say such a thing, his reply was, "I don't think there should be a single boot on the ground over there. The only way to fight that war is the way we do it. Drop out of the sky from 50,000 feet, unload all of the ordnance and hit the afterburners the heck outta there!" He had three tours in Nam at that point and he was dead serious. "Any man who wants to go to Nam to fight is a Goddam fool!" he said. He was a brilliant USMC officer, with a geat deal of war experience from WWII, Korea and Nam. Today, I believe more than ever before, that he spoke great wisdom then.