Eragon comes off as such a small person when he kills that captain. That speaks of his insecurity; it's like he's the neighborhood bully. When someone makes fun of him in any way, he can't respond with his own cleverness--he has to use brute force to get the message across. Eragon is nothing but a meathead.

There's also the obvious "Join me or die" thing--he couldn't compromise with these people. He couldn't promise to not kill their Lady and in fact find some way to get her out of her oath. After all, it's just so much less work just to kill them right here and now--what use is gathering support when you can just force people to join you or kill them?