Perrat acted in a manner that I believe anyone would to protect someone they'd care about. His actions could be explained as a poor assessment of the situation at hand or he'd acted on instinct. Although Vasser did make herself as strong enough to win against Kyte, that condition did not necessarily include making her invincible. Yes, she could've dodged the arrow or even healed herself, but there is also the possibility of her having been severely injured leaving her incapacitated and therefore incapable of healing herself through her powers. Kyte also entrusted Vasser to Perrat, which might also be a reason why he protected her. This is why I believe that Perrat isn't annoying or stupid, but rather just an intelligent man who acted instinctively to protect someone he cared about.
Am I the only one who finished chapter 63 and thought ' fuck, perrat is annoying', she probably could have dodged that, the guy just blocked her sight. Annoying in the sense that this guy really laid it all out for somebody who not only doesn't care about you like that but also could have handled it. Gotta shake my head on this one, don't really feel bad for him, as a character he kind of just misses, if they took him out the story I wouldn't have even noticed. (● ̄(エ) ̄●)