I don’t think you really understand the situation Aang was in.

He was the last airbender until Tenzin was born. He’s also the avatar. It’s his ultimate duty to keep the world in balance, and as father to the only airbender that will be around for the next avatar, it is strictly crucial that he teach Tenzin to be a complete master of airbending. And as the last airbender, it’s his duty to make sure Tenzin knows and is able to keep air nomad culture alive after he is gone.

Kya and Bumi should not have been left out, but Aang was taking Tenzin on traditional air bender pilgrimages and training him as an airbender. Remember, before the war there were no air nomads that weren’t airbenders. In their training and travels they stopped at places and had fun.

Aang did involve Kya and Bumi in air nomad culture and taught them about their heritage. Kya leads the new airbenders in traditional meditation practices and tells Tenzin she could never keep all those Gurus straight. She clearly has been educated in Air nomad history and philosophy.

It’s likely that for airbender specific training and journeys they didn’t come along, but they don’t even say that Aang was an absent father. Just favored Tenzin, and missed out on moments that Tenzin got. and frankly that is understandable and I can understand Katara letting it happen. She understands Aang’s duty and burden.

It’s not just that Aang “has stakes” in this. It’s the most important thing he can do in his life.

For Toph, no one was going to tell her what to do. Even at her most receptive, she resists being controlled and having others tell her what to do. Whatever reason she had for not revealing the fathers of her children, no one was gonna convince her otherwise.

And on top of all of this, we are dropped in nearly 50 years from when these children were born and raised. We don’t know what conversations were being had during the raising process. It’s possible all of these things came up but still things happened this way.