Ah, yes, she would have, but that's because she's human and she's rarely had to fight alone. Arthur, on the other hand, has been fighting alone for a very, very long time now. Relying on others is something he hasn't done since he last fought in a proper Holy Grail War.

Arthur quietly accepts the scolding, respectfully not interrupting her until she finishes. She has a point, of course, but she also doesn't know anything about his situation, how he came to be in Chaldea, and he's not about to tell her. Instead, he gives a shallow bow to her, because while she is not his Master now, she will be one day and he made a promise to someone else to keep her safe. Respecting her feelings and her concern for him, no matter how unwarranted he finds it, goes hand-in-hand with that. She's only trying to help anyway.

"My apologies. You are correct." He gives her a warm smile. "I will take Gawain along next time. Would you worry less then?"