The smart thing to do would have been to take the given opening and play dumb. If he let the Red Hood lecture him on what he thought he knew of the League, Damian would have been able to tell just how accurate (or possibly outdated) the other man's information was. He either knew the League by reputation, had former dealings with them, or possessed a skill set on par with the league, themselves (given how he was still alive and standing here.)
However, Damian couldn't help bristling at the implication that he was out of his depth. His eyes cut sharply to Laura for a moment, again questioning her motives in his affair (was she helping him? criticizing him?) and rose to the bait.
"I know them better than you do," he spat back, his voice a mixture of defense and irritation. As he spoke, his palm pushed down on the end of his sword just a bit.