I'll have to agree with him on that point. I never understood Democrats who said that.
My guess it's leftover feelings from the way soldiers were treated when they returned home from Vietnam. They don't mind being associated with the anti-war stuff, but do mind being associated with people who throw garbage at individuals.
It's simple: if you don't support going to war, you still may hope for the success of the war once it's been decided upon. Even if you don't even support the mission to that extent, you can still hope for it to conclude with a minimum of bloodshed, especially on the part of our soldiers.