Here's my thoughts about why Amon didn't kill Korra when he had the chance.
His plan is likely to take away all bending, for all time. I don't know what his plans are for the general populace, but the most prominent bender is the avatar. The thing is, if he kills Korra, she will just be reborn somewhere in the earth kingdom - and probably hidden from him this time. He needs to end the avatar cycle completely. How can you do that? By killing the avatar in the avatar state. Korra has so far not been in this state at all, so Amon has held off killing her. He simply will wait until she is channelling the avatar spirit and kill her quickly.
Getting to her quickly even in her powered-up form probably won't be too hard for him. He is good enough at dodging that I don't remember him ever getting hit by a bending attack. We have also seen him resist bloodbending, so he might resist other bending powers as well.
Does Amon know that killing an avatar in the avatar state ends the cycle? Not necessarily. That is something we only knew Aang to know - but then energybending was a skill only Aang had too, so it's not very farfetched.
What do you guys think?










