We see Aang willing to accept a total change of a sacred, traditional Air Nation celebration to make it more appealing and more modern for everyone. For the Acolytes, who can’t bend, for the towns people, who don’t consider themselves Air Nation. And for Sokka, who loves eating meat–something that goes against the Air Nomads’ strict vegetarianism.
He was willing to change his ways and his culture to fit just friends and a bunch of strangers.
Now, if you think for .01 second that he wouldn’t be willing to do this for his children, or that he was disappointed if his children were not Air Benders or vegetarians or if they did not fully accept every little Air Nation religion/tradition then you. don’t. know. Aang.
Bumi didn’t live up to the Air Nomad culture of violence-free, peace advocacy by joining the Army, but he kind of did, by joining with the purpose of protecting the world and upholding the laws and values his parents dedicated their lives to creating.
No, Kya did not accept the Air Nation as her own nor took any apparent interest in their culture, but she kind of did, by embracing her nomadic heart and a clear attraction to the spiritual side of life.
And Tenzin. Dear Tenzin, who tried so hard to continue to Air Nation, but lived by the Water Tribe values of family and love.
His children may not have been what he expected, but if you think for one second Aang didn’t love and wasn’t proud of each one of them, you're wrong.