Shepard is the sort of person that makes Quintus' life that much more difficult. She's the sort of hothead, in his opinion, that in the thick of the moment can convince themselves that they don't have much to lose, and one can't really bargain with a person like that. He's resentful of the special treatment offworlder Tributes have gotten in the past and absolutely sees her as the sort of person that you should not give leeway to, because if you give an inch they'll take a mile, and while he recognizes her combat ability the idea of having her out and potentially within the rebellion's grasp doesn't sit well with him.

And yes, the fact that she's been friendly with Tabris doesn't help. XD