In this question, Korra was apparently about 6 years old or so when the Order of the White Lotus discovered her and formally recoginsed her as the avatar. Before that, she was just living in the south pole with her water tribe parents.
It's reasonable that she could have learned water bending from her father, who is shown to be a waterbender in season 2, but how could Korra have been able to bend earth and fire at that age without any training?
Aang was 12 years old throughout the events of Avatar: The Last Airbender, and at first only knew airbending (avatar state notwithstanding) because he was raised and trained by airbenders. He had to specifically seek out masters from other nations to learn the other bending skills, he wasn't just born with the knowledge to waterbender or whatever.
Also, in season 3 of Avatar: The Last Airbender, there's an episode about Avatar Roku's life, who also didn't bend more than one element before discovering that he was the Avatar and tracking down teachers to learn to bend the other elements. This sets a precedent (of only two Avatars vs. one Avatar, admittedly) for Avatars generally only learning to bend other elements after seeking training.
So how come Korra is different? How could she know how to bend earth and fire without any training?
From comments and answers, I can see that the out-of-universe reasons are being focused on, which is interesting and all, but I was more interested in an in-universe explanation. How can she learn to bend earth and fire without teachers? Aang needed teachers...
Were there teachers I didn't notice? Was there a firebender or earthbender living in the south pole? Or is there any other established in-universe examples of people learning bending all by themselves with no teachers or examples?