Romans 13 and why it doesn't mean Christians should be in the army

I've never made a secret of the fact that I don't think Christians don't have any business killing other people. By far the most common objection I've heard to this belief that Romans 13 allows it. I have two counterarguments to that.

First, that's allowing those few verses to override the entire tenor of the New Testament, including the example of Jesus Christ himself. That's what cults do, and to elevate one part of the Bible as more important than the rest sets a dangerous precedent.

Second, that's not what it says anyway. Paul's epistle to the Romans was written to Christians in Rome, and is mostly in the second person. That is, it's as if he was talking to the Romans. At several points, however, he switches to the third person; he's talking about someone. He's not writing to Christians who bear the sword, but to Christians about people who bear the sword. That's a big difference.