Unrealistic plot scenario (Spoiler)

The private investigator kills Julia's girlfriend Matty, because she caught him at Julia's apartment. That's not something a private investigator in real life would do IMO. He would have come up with some excuse (possibly even telling the truth for why he was there). Then again I guess if he didn't kill her you wouldn't have much of a movie.

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*I know that I am stupid but when I look around me I feel a lot better.*