I'm interested in a more detailed reply to this as well.
Offhand, I am reminded too of King David and King Solomon. King David had God's blessing to do what was necessary at that time, it seems, but even so, his hands were too bloodied to be the right one to build the temple.
We have Saints who are soldiers as well.
So clearly, being a soldier is not itself condemned. I suppose at times, perhaps God's hand needs to work through men on earth to protect others? I'm only guessing.
But there is an ethos too of not killing, no matter what. Unless I am in that position, I cannot say what I would do. (I was trained to fire a gun and once the decision is made to do so, there is no thinking about it, so that is in there. But on the other hand, my heart is strongly turned now to harm no one, ever, in any way, if I can prevent it.) But truthfully, I don't know, what I personally would really do, in an extreme situation.
Priests and monks, though, have taken additional vows, are more responsible in a sense, I think. And priests in particular care for the souls of others (many monks may end up doing so as well), and priests consecrate and distribute the Eucharist. If hands that had been bloodied were too soiled to build a temple, would bloodied hands be too soiled to handle the Body and Blood of Christ?
These are just my thoughts. Don't take them as an answer. I don't know for sure the thinking behind it. But you ask an interesting question.