"Give up? Heh." Aaron scoffed. "You have known my family for a long time now, uncle Leo. Do you really think that we give up without even trying? The Colemans won't back down just like that." He might be complaining about a lot of stuff, but that does not mean that he won't actually do it.
For Leonardo to say that to him, is making him feel irritated. From his point of view, it seems like Leonardo is looking down on him. His pride is hurt when he thought of that. He came from a prideful family, and this is the way his uncle Leo is seeing him, then if that is the case, he will make sure that Leonardo will regret looking down on him.
"Let's see about that." Originally, he was only making sure that Nathalia and Aaron didn't hear his conversation with his wife, but now that it has come to this, he would like to test Aaron.
A test that could make him see how serious Aaron is about the organization.