He doesn't fully grasp the way the Ministry is trying to cover things up, or how they scheme against him and will do so more still if he doesn't shut up. And more importantly, he's being too angry to be very receptive to subtle messages. McGonagall cutting him off really doesn't help there. She should have told him more clearly that she knew he was telling the truth, entirely believed him, that he had her full support, yadda yadda, but he was better off just keeping his head down around Umbridge and ignoring her lies, that he ought to consider it a challenge in self-control, and so on. Harry leaves that conversation being mad at her for siding with Umbridge, which couldn't have happened if she'd dealt with things properly and made clear she was on his side.