“It just wasn't very believable.”
You watched a movie. You weren't able to enjoy it because you thought the characters and the setting were too unrealistic. You're discussing the movie with your friend, and you say this.
It just wasn't very believable.
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"Just not" expresses the feeling that, even though you want something to be true, it's not true in reality. There's a phrase that was made famous by the TV show "Sex and the City", and later used as the title for a movie:
Being "into" someone means that you like them a lot. This sentence was told to a woman who was worrying about why a man who she'd gone on a date with hadn't called her back. When she heard "He's just not that into you," it convinced her to stop worrying about it.
(a story) (is) believable
The word "believable" can be used to describe a story that's realistic enough for you to accept. When you see or hear it, it makes you feel like it could be real (although you know that it's not real). "Believable" is mostly used to talk about stories like movies, TV shows, and books. The opposite of "believable" is "not believable". You've probably heard the word "unbelievable", but that word means "amazing" or "wonderful", so its different from "not believable". People don't use the word "believable" to talk about stories, explanations, or descriptions of real events. When someone describes a real-life event and you think that it might be true, you say that it "seems plausible":
That seems plausible.
When it seems like it probably isn't true, you say that it's "not plausible":
Yeah, he says that they agreed to pay him five thousand dollars, but that just doesn't seem plausible.