The NFL's 2009 national tournament resolution, "Resolved: military conscription is unjust," is deceptively simple, but in reality offers a wide range of options for both sides.
Although it always seems weird to me to affirm a negative statement, that's what the resolution demands, so that's what we have to do. There are at least three overarching positions to take, with options under each.
1. War is itself unjust, so anything that promotes war is unjust. (Pacifism.)
Corollary: Even in peacetime, the draft increases militarism and ethnocentrism, which leads to further conflict
2. Military conscription is instrumentally unjust--in other words, it leads to unjust outcomes.
a. It ruins society or otherwise decreases social utility.
b. In practice, it is unfair or exacerbates social division.
3. Military conscription is intrinsically unjust, violating liberty / autonomy / dignity / rights. (A deontological framework.)
1. In response to pacifism...
a. Just war theory, linked into notions of national self-defense and the necessity of conscription
b. Argue for the moral necessity of war, and that social benefits, to be fairly deserved, should be fairly won
c. Argue that it unfairly broadens the resolution and is a time-suck.
2. In response to instrumental arguments...
a. Attack utilitarian notions of justice (although this might be tough for the Neg to pull off)
b. Agree with utilitarian premises, but show how they lead to the opposite conclusion
3. In response to rights- or liberty-based arguments...
a. Deny the framework, and fight back with utilitarian, communitarian, or other notions of justice
b. Accept the framework, and show how the draft does not violate liberty / rights / etc., perhaps via social contract reasoning (Rousseau might be good here).
Of course, there are other less traditional approaches that might work as well. Feel free to suggest your own in the comments.