@leusee
A "date" is just an event people do together. It's not explicitly used for finding a relationship partner. I feel like girls tend to use the former definition more freely than boys do. So, boys will "hang out" with their friends and girls will go out on "dates" with their friends. The confusion come in the application of it usage and boys tend to only think about the "dating to become a couple" aspect. Having a date, especially one that was interrupted, doesn't mean your "dating" or a couple yet.
Obviously, that's a generalization between the genders, but an accurate one.
I don't get the "harem" fear. She rooting for the MC to date the other girl and made it clear that this "date" is them "hanging out", so he doesn't make the same mistake he just did with the original girl. She's asking about comparing mouths because she's a self conscious high school girl. No different than asking about her figure. And he just happens to be able to compare.