Star Trek is science fiction, period, end of story, it isn't up for debate. They had nasa consultants working with the tng showrunners for quite a while to make sure that the science of the day at least seemed accurate or plausible even if the explanation given isn't exactly scientific fact. Of course they did stuff that most likely isn't possible and explained a lot of stuff wrong.... that's where the "fiction" in science fiction comes from. Many of the underlying principals in the show are factually accurate though, or at least were factually plausible at the time. Much of the tech in the show, for example, is now actual stuff that you have in your living room and use everyday. Transporters.... yup some scientists have managed to "teleport" a few atoms across a room. Scifi isn't about what is, it's about what potentially could be.
Science fantasy are shows like Doctor Who, where they have flying sharks because flying sharks are cool, or Star Wars, where they don't even bother to attempt to explain how most stuff works, ect...
I've said my piece and now I'm leaving this thread as a warp core breach between you two seems imminent.