I don't usually do down this route to defend characters' actions, but since I'm anyway continuously reminding myself of the fact Yukio is the younger brother of the two, even being ready to shoot his brother is not out of the question. Furthermore, he has been brainwashed taught by the exorcists since very young age, making him more easily impressed by the real powers and distanced from Rin. I reckon he's genuinely divided between saving his brother and saving the world as equally worthy causes. In fact supporting Rin even this much already goes beyond what many kids in his position would do, considering real or imagined (since not so many yet know who Rin really is) pressure from outside.