I don't think it is a point of giving up Katara forever (and know I don't ship).
I think what is being conveyed here is that Aang has to give up his devotion to Katara as his number one priority.?? Afterall, he promised her he would not go into the Avatar State anymore because it scared her (in the Avatar??State episode)??and he also promised her he would not use firebending anymore after he hurt her (in the Deserter episode).??
Aang's destiny is being blocked by the commitments he has made to Katara.?? He is being stifled from his full potential by allowing her to be first in his thoughts.?? So does this mean he will give up his love for Katara, I don't think so... but I think he needs to come to the realization he cannot keep his promises to her AND save the world.