What determines a bender's element? According to the show, it depends on two things. One is the environment your born into. If you're born around other Waterbenders or in a specific tribe of people, that will determine your element. The second thing is your mentality. An Earthbender will not be born in the Water tribes because the characteristics of an Earthbender do not thrive in those environments. The same applies to all of the elements.
So in short, your bending element is determined by the environment in which you're born, and your mentality (which grows in the shape of your environment anyway).
Its obviously not based on genetics, because Katara had two nonbending parents, but she WAS born in a Water tribe and had the mentality of a Waterbender.
Until the show states otherwise, this is the safest answer to assume.
