If a FREE country decides to invade another country, aren't they forcing people to fight and die who do not want to?
It's not free. However, it is less hypocritical, since it is treating the nation's own citizens similarly to the way it is treating the citizens of the other country.
I think a lot of the people in favor of the draft right now think making military service involuntary would simply prompt more citizens to face up to the impact of war in more immediate ways. As a consequence, they expect opposition to the current wars to become more galvanized. Personally, I'm concerned that tactics of this sort seem always to have unintended consequences that end up making things worse instead of better. That is why I'm cautious about it.
However, I don't find your argument about freedom convincing. It is putting a higher moral value on our own citizens' freedom than on the freedom of others.