"I know it’s hard, but it’s for the best."
Maybe I am just imagining things, but to me the scene with Meelo and Tenzin felt like a huge metaphor for loneliness that often comes with power. Being in such a powerful and important position as the Avatar (or in case of Aang and Tenzin; being the Last Airbender) can be very lonely. Many people put their faith and trust in them, while they have to learn to control the elements, ensure peace, find their inner balance or save the continuing existence of a whole culture. Yet they are only human and need a family and friends, someone that loves them no matter what. Finding Balance between the task of being the Avatar (or Last Airbender) and the longing to settle down and live a normal life must be very difficult. Avatar Roku died and caused 100 Years of war because he was indecisive and trusted Fire Lord Sozin too much. Aang ran away because of the pressure and expectations he already felt as a child, and was not there when the Fire Nation killed the other Air Nomads; people that were like family to him. Korra feels constantly betrayed and deprived; even if somebody only has the best intentions and wants to help her. And then there’s Tenzin - His father was the Avatar and he himself was the Last Airbender for a long time, indirectly caused hundreds of years ago by Avatar Roku, which separated him from his siblings. He knows how hard it will be for Meelo, Ikki, Jinora and Rohan one day, since a whole culture depends on them.
Being the Avatar/Last Airbender makes you lonely, because you are different. There is no one like you in the world, no one with such a power, no one with so much pressure on them; and that will always separate you from others. I don’t think it’s coincidence that most Avatars best friends were animals; since they are always loyal, good listeners and would never judge or leave you.
As Avatar Yangchen said to Aang: “Selfless duty calls you to sacrifice your own spiritual needs and do whatever it takes to protect the world.”