Yeah, it's definitely got some genetic linkage, but not in any sort of readily predictable way -- we've seen cases like Sokka and Katara where you have both a bending and non-bending sibling, and both Kat and Haru are clearly cases where bending kids have one non-bender parent. Isn't there even an episode back in S1 or S2 where there are a couple of identical Earth Kingdom twins where only one is a bender? So it seems like there's some weird hand-wavey spiritual aspect as well that's never been entirely explained. They've also never really addressed what happens if you've got intermarriage between nations (and c'mon, in a hundred years of war and occupation of large parts of the Earth Kingdom, you know there's gotta be at LEAST some Fire/Earth marriages going on; and the clothing styles and eye colors and geographical location of Kiyoshi Island make me think there's maybe been a little Water Tribe influence there at some point...) Some fan-writers have gone for mixed-bending skills but that strikes me as dangerously Sue/Stu-ish, and sort of dilutes the uniqueness of the Avatar being able to master all the styles. My personal fanon is that such kids would only have one bending skill, but you might have siblings taking after different sides of their parentage.
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