I was wondering if it would be a sin to avoid the draft, by moving to Canada or Europe, assuming the draft was enacted. Not if you had a moral opposition to war, but simply because you view a particular war as an inconvenience or as a waste of time or as a dumb war.
As Catholics we are called to respect civil authority and to follow just laws; only when the civil authority passes unjust laws are citizens allowed to disobey them. If a state legitimately determines that citizens are needed to help in the prosecution of a just war, then for citizens to avoid that responsibility without just cause would be unjust. For more information on the Church’s understanding of the just war doctrine, see the link below.