There's a lot of pressure in being the Avatar -- not to mention the terrible dinguses goading her to feel worse. Tarrlok called Korra a half-baked Avatar-in-training, mocking her because she hadn't mastered airbending. Hey, Tarrlok... did you master three elements? Then shut your mouth! But that remark stings Korra; she really is frustrated that she can't airbend, much less reach the Avatars of the past. In her own words, she's a spiritual failure.
Being the Avatar is what she's been training for for most of her life. It's what isolated her from the rest of her friends and family. So not being able to master it, especially when the world needs it, is a sign of utter incompetence in her eyes. What makes it more sad is that even now, when Korra has a group of friends dedicated to being her family, she still feels like she's alone. Team Avatar -- that's Korra's friend group, with Asami, Mako, and Bolin -- is there for her, though, despite what Korra thinks.
And that's important. They've got her back even if she doesn't know it. We see that in an episode late in the first season; the writers are really nailing that "importance of friendship" theme. It's *sniff* beautiful. And it's a theme that will make you (and me) cry continually throughout the entirety of the show's run.
If you're not familiar with the first season arc of Korra, let me set things up. Equalists -- folks who think bending is oppressive -- are trying to revolutionize Republic City, the main city hub. Their leader, Amon, is The Worst. Basically, he tricked his followers into believing that he had the ability to remove a person's bending abilities. And he could, I guess, but it was because he's waterbender--a waterbender who used bloodbending (GROSS) to rip a person's connection to bending away.
In the episode "Skeletons in the Closet," Equalists have taken charge of Republic City. There's basically a war between those who support the Equalists and those who don't. But in the middle of all this, there's this moment between Korra, Mako, and Tarrlok (also The Worst) that, ironically equalizes everyone on an emotional level. Tarrlok tells Korra and Mako that he's Amon's brother. He tells them the tragic backstory of why Amon went bad.
Turns out Aang -- the Avatar before Korra, if you've forgotten already -- took Tarrlok and Amon's father's bending abilities before the brothers were born. So when Tarrlok and Amon (then Noatak) were born as waterbenders, his father went fucking nuts. He trained them to be bloodbenders, not only practicing on animals, but on each other. Let me repeat that: Tarrlok and Noatak's father made them practice bending the blood out of each other. What the fuck.
And, I mean, if that wasn't bad enough, just wait. There's plenty of fighting, and some stuff with the Avatar -- I'll get to that -- but Noatak eventually escapes on a speedboat with Tarrlok. Here's the thing: Tarrlok is mean, but at least he feels. He's about to do something that he has to do. For a bit, he kind of goes along with Noatak's celebration that together, they--as brothers--can do anything. Anything, as in, take over the world or something. Tarrlok feels. He feels that Noatak has gone too far. So he ignites the gas tank on their boat they're on.
And you thought your family was messed up.