Sean Ambrose: You know women, mate. Like monkeys, they are - won't let go of one branch until they've got hold of the next.
Ethan Hunt: You turned around.
Nyah Nordoff-Hall: What are you going to do? Spank me?
Sean Ambrose: In just a few hours you can be assured of going down in history as the typhoid Mary of "Aus." G'day.
Answer: Ethan did not want her to kill herself. Giving her a gun would allow her to do so.