Light had betrayed Rem; he had caused L and Watari to be the threat to Misa. So why didn't Rem kill him as well?
Rule XXXIV.3 of the Death Note states:
Only a god of death that has passed on their Death Note to a human is able to kill the owner of the Death Note.
Although Rem had earlier passed Gelus' Death Note to a human, "Light has Ryuk and Rem possess each other's Death Notes, so Ryuk is tied to this notebook for the remainder of the series". Thus Rem could not kill Light, because she had not passed on a Death Note to a human.
This is the answer I have pieced together using this Quora answer and the above-linked wiki page, but it doesn't sit well with me. I can't see anything in the rules that states that if gods of death exchange notes, then the notes they have passed on exchange ownership. Rule XL.3 states that a god of death becomes the owner of a death note they pick up, but the surrounding rules' context would seem to indicate that this only happens if a God of Death dies.