I have met several children and teenagers who act the same way Korra does at times. Parenting and the environment you grow up in fosters different behaviorism. As others have pointed out, Korra being thrust into "you're going to save the world" mode from being a young child got to her head. Anyone who is isolated far from any other life (aside from your tribe, and those who train you) would probably adjust the same way she has.
I will admit that sometimes I dislike Korra. I don't think labeling her a mary sue is correct though, as someone else pointed out, mary sues often do not have flaws. I think what we have is a character who is very stubborn and headstrong because of her upbringing. However, I can relate to how Korra feels and her frustrations. From her perspective, not only did her
father get thrown into jail for something he did not do, but her own uncle used her and betrayed her trust/faith. Sure, she was quick to drop Tenzin, but I account that for her inexperience. Often, the people who are sheltered can be quick to jump at any opportunity present, if they aren't satisfied with their current situation. She was feeling unhappy because she wanted further training from Tenzin, only to be told, "You are not ready." Whether she may or may not have been ready is irrelevant.
Anyway, getting back to her perspective. Not only were her parents put on trial, her father thrown in jail, and her faith in her uncle destroyed, everyone she turns to basically refuses to help. It's been tossed around in the season that the avatar should remain neutral, but I think almost anyone in her shoes (when it is about your own family) would probably drop that mindset quickly. So she goes to the president because she doesn't know who else to ask, and he blatantly refuses to help her. I can understand that not every government official can do things (The USA probably wouldn't have jumped into wars previously if we weren't attacked somehow). But after dealing with that frustration, Mako sidesteps her the same way he is doing to
Bolin and then dumps her because she is frustrated with his neglectful attitude.
Then after all of this, she ends up having to deal with everything on her own, gets eaten by an angry spirit, and loses her memory.
Korra has had it rough, and while I am excited for her amnesia (and potential character development because of it), I think everyone needs to cut her some slack.
In the spirit of friendly debate, I offer my own opinion above.
I can agree with most of what you said. Except for the fact that, you imply with your statement, people who like Korra (and her behavior) are non-thinking followers of the show.
I don't think stripping Korra from "mary sue" tendencies has destroyed her character.