To tack onto to other people's point: the Warrior is someone who died and willingly came back. He has given up his own body for this crusade. If he had moral compunctions before, he likely has lost them all now. For everyone else, this is round 1, for him this is round 2, and there is little to no room allowed for error. What does he have to live for after killing the Demon King anyway? The Hero's mistake here was trying to appeal to him emotionally. Likely if he made an argument, 'even if she was mentally weak, her utility eclipses that', that'd probably have breached the Warrior's cynicism, but at best it'd just make him consider it. Without a realistic or viable plan to get her back either, which the Warrior has little motivation to think up himself, again, he wouldn't consider helping her. Further, from his perspective, his two greatest assets to kill the Demon King are possessed by people who themselves are liabilities, so he has less inclination to listen to them in the first place.
The Warrior is a man on a mission, and he only puts up with the Hero right now because he has a very useful Body. It is the mistake of his party, and frankly a sign of immaturity on their part, to not recognize how far gone the man is, but to be fair to them, they are literally 16, when I was 16 I wouldn't know how to convince a deeply traumatized 30 something to help me either. Especially in a world that so actively punishes empathy.
This isn't to say saving the Cleric on an emotional basis is a poor argument, but it just wouldn't work with the Warrior as he has so far been written. This is such a marvelously well written inter-party conflict.