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Continuity mistake: In the car chase scene with Nyah after they split and hit again and are spinning look at Ethan's car. The driver's side in the close ups was on the American side, then in the spin it is reversed to an English side. (It is a negative image - the license plate is reversed). The next image is back to normal.
Answer: Ethan did not want her to kill herself. Giving her a gun would allow her to do so.