Why would he want another duel when he know she didn't learn any swordsmanship

I'm guessing for one he's falling for her, and also, even though she didn't have any training, she wasn't just beaten by him, so maybe he wants to see that again ┑(￣Д ￣)┍
I mean he was pretty surprised that she didn't grow up there and "still got that much skill" :)

Yeah but even if she can defend herself it's still unfair
But he is a kid so maybe it's just so he can see her again