[Gokudera does not like anyone older or younger than him, and being around fifteen or sixteen means that twenty-three is old. Even if she isn't.

He's very much not a grown man and has no idea how to talk to women.

If he says yes, that makes him sound like a jerk. Saying no means that maybe he targeted her for whatever reason and he didn't. So he just stares at her with a sort of nervous, dumbfounded expression. That is a trick question, isn't it?]

Ah. Tsukuyo-san, then. Maybe you should wear a nametag if you're going to tell people what to do and expect them to know how to respond.