"Yes you are!" Morgana doesn't care that she's lying. She doesn't care that poor Arthur's ego might be crushed. Keeping him here, in the palace, is more important.

"Can't beat me with a sword. You couldn't be a squire until now." She's implying it's because he's not capable, though it's obvious to everyone that Uther did it for protection.

"I'd be more useful. Maybe I should go, instead of you."

Insulting enough for him?