Why did Luther drop his coat at the end of Season 3?

Alice Morgan tells him to lose the jacket.

Yeah, Alice has been trying to get Luther to leave the force for so long and Luther does it at Alice's suggestion, because the jacket is his work, his staple.
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Throwing the jacket represents that he is done with his violent life.

We as an audience have only seen one side of Alice before now, the psychopathic and non caring side. Much as most of the characters have only seen the one side of Luther. Leading to some, such as Stark and Grey, to assume he is responsible for his friends deaths. We as a viewer are also to assume Alice is, although protective of Luther as we see in Series 1, uncaring for other human lives. Perhaps Cross wrote her the way he did in this episode to show us how we have been so wrong about her, as Mary practically words nearing the end of the finale: “I don’t care what she’s done, John, she saved my life”.

So it would seem appropriate that Luther chose Alice over Mary, and walks off into the sunset with her. Although it was quite fitting,him throwing his coat away into the river signifies him letting go of his life as a copper.
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