I thinks the wings is some kinds of symbolism like the angle dream or something and when people in so deeply in love they will try anything to cut loose of the other person dream in order to keep them from flying away. How this story end implied that the way to your dream maybe lost but it never forgotten and if you truly love someone you keep them with you, you fly away and carry that person so that there are no leftover. But I don't like how the author decided to went with this route of violent, they could have been done by thousand other ways. Thus I think she(just my assumption) mainly chose this way of approach because she want to show us that despite how purely love is there will still some toxic exist in it.