The analogy I would like to offer is one of a person who enters into a contract with someone else. If that person later decides to break that contract, then they are in breach. Normally (in real life, anyway), there are penalties. If a person borrows money from a bank, and then cannot pay it back for whatever reason, then that person has broken a contract and penalties are enforced. There is plenty of precedent for this.
So, a person may argue that the armed force (in this case) has not put a commitment in as perhaps a bank, which has lent its money out. I would argue that no, the armed force has indeed made a commitment. In some cases, that includes education (paid for in exchange for military service, or even in teaching a very marketable trade, such as a vehicle mechanic or what have you). As well, given that some potential recruits are told to wait until availability, the net result is that the military force in question loses out.
In any event, people who joined the US forces after say February 2003 don't have a leg to stand on when it comes to "CO" status. Do your time and then get out is one option. If your objection is really related to concern for your personal safety vice the moral conduct of a war, then I would suggest that said person is a coward.
Cassius Clay (aka "Mohammed Ali") was drafted (against his will) and had a moral objection against the ongoing war in Vietnam, and I believe against military service in general. In any event, he went public with his objection and faced his consequences, knowing full well what they were. That is what takes courage, in my opinion, much more than running away and then spouting off in public once you are behind a (real or imagined) wall.