fwiw, I hear that it's not actually too insane in Japan to enter a love hotel for not-fucking, since it's an easy place to get a private room for cheap at hourly rates (so some will turn away same-sex couples if they suspect they're just there to hang out / whatever vs actually like, using the hotel for their own purpose). So them wondering about the other's "ulterior motives" isn't entirely insane (though, in the context of just going so she could wash out a contact, that seems like an overkill reason to book a room, tbf).
On another note, it's very funny to me how he thinks An is so mentally unstable that she'd go "oh no! I was taken to a love hotel! Quick, the only way out of this is to immediately kill myself."