one of my favorite things about tlok is that it makes it clear that producing more children doesn't automatically sustain a culture. i remember someone noting a while back that tlok does a good job of highlighting the difference between obsessively trying to sustain culture and thus accidentally cultifying a movement (tenzin), versus sustaining a culture through teachings without necessarily relying on breeding to initiate new acolytes (aang).
and yes, bumi and kya thought aang loved tenzin the most bc he was an airbender and they weren't, and they have a right to those feelings because they're not aang. but they don't know that by choosing to be with katara, aang chose them (via katara) over what others perceive as his duty to air nomad culture (reproducing with multiple women and starting a non-traditional family where the children are not necessarily raised in a nuclear family).
tenzin went the reproduction route, and he got lucky every time that his genes were strong enough to produce an airbender over and over again, but he too learned that genes don't make the culture! when korra struck balance, the cosmos decided to make air nomads everywhere instead of just on tenzin's island. because culture itself can't only be sustained through blood.
i keep thinking about this now that the new movie's coming out bc i think it's still very thoughtful that aang stayed true to his love for katara over literally everything else. and i know that if she had said no to having his children, he wouldn't have pushed her, or gone out and made children with women willing to carry the avatar's baby. because that's not aang! it has never been aang. aang's journey was coming to terms with being the last airbender. there was never any expectation that he would reproduce, because little homie thought he was gonna die when he fought ozai. even at age twelve, he knew that knocking up a hundred women wouldn't have magically revived air nomad culture.
for aang, the only way that could be done was through consistent teaching and sharing of values, and that's precisely what he ended up doing. i don't think bumi and kya are oopsie babies at all. i think that was tenzin. i think aang and katara had bumi and kya because they wanted children to love and to hold, regardless of what kind of bending they did or did not have. they had those kids on top of their duties to the world and to their respective cultures and people. tenzin was a true miracle, but i don't think it was an intentional move to produce an airbender. i think they just had a damn baby like everyone else. in truth, i believe aang made his peace with being the last airbender when he chose katara over cosmic energy. bc at the end of the day, all the love he lost through the air nomad genocide, he got back through katara.
very different than how tenzin went about sustaining air nomad culture. tenzin wanted the family and the babies, and he got it all. and still it was not enough for tenzin, because it took tenzin over fifty years to understand what aang understood the moment he realized he was in love with katara. blood will only take you so far. to forge everlasting bonds beyond blood relations, you have to have friendship and mutual care between each other. and tenzin struggled deeply with this! he had his wife and his kids, but he barely had any friends that wasn't his ex-girlfriend from twenty years ago, and he didn't like his siblings who were literally his siblings, and not random people off the street. but they weren't airbenders! it's one of the saddest things about tenzin's character that never truly gets resolved bc he really spent all that time away from his siblings and mother because... they weren't like him. even though his father chose his mother over cosmic energy. i truly do think if aang was still alive, they woulda fought.