The following contains spoilers for AVATAR: THE LAST AIRBENDER and THE LEGEND OF KORRA.
“I’m the Avatar, you gotta deal with it!”
With these words we were introduced to Korra, the hero and main character of The Legend of Korra. What an intro, seeing a little kid bending earth, water, and fire. She was completely different from Aang and had no problem letting you know it. Despite her massive amounts of confidence however she still had trouble bending the element of air. The other three, no problem, but even into her late teens, airbending seemed impossible. This is what led her to Air Temple Island to be trained by Tenzin.
Why was air bending so difficult to master for Korra? If she could learn the other three elements by the time she was a kid, what made air so hard? There are two reasons, one in universe and one meant purely to differentiate Korra from Aang.
An in-universe explanation is given in the second episode of The Legend of Korra, ‘A Leaf in the Wind.’ Korra expresses her frustration with airbending and Tenzin explains that, “often the element that’s the most difficult for the Avatar to master is the one most opposite to the Avatar’s personality.”
From the moment she was introduced Korra was hotheaded and raring for a fight. She didn’t take “no” for an answer and was more likely to punch her way through a problem than talk it out. It makes sense the other elements were relatively easy for her while airbending, an art that focuses on indirect styles of combat, didn’t come to her as quickly.
Aang had similar issues when it came to earthbending since it was in complete opposition to his personality. Aang wasn’t like Korra, he didn’t tackle problems head-on. Especially in the first season he often solved problems with a calm air and sometimes a joke in tow.
This leads to the second answer to the main question we’re discussing, one that made it so Avatar: The Last Airbender and The Legend of Korra wouldn’t be too similar. Seeing Korra learn all the other elements, as Aang did in ATLA, would have been repetitive. The shows creative staff wisely realized that by aging Korra up from where Aang started and making her naturally talented at the three elements he had to learn, they wouldn’t be giving the audience the same stories they’d already seen. It would allow them to show the process of learning air bending, a process we had seen little of in ATLA.
It also helped inform Korra’s character. When crafting the sequel series the team behind it didn’t just want to repeat ATLA beat for beat. They wanted something new and the idea of a hotheaded Avatar contrasted nicely to what the audience had seen with Aang.
It also helped round off the “Book” titles of each season. The original series’ seasons had been given the titles of ‘Earth’ “Water’ and ‘Fire’ respectively. It made sense to have the first season title of The Legend of Korra continue this with ‘Air.’
So there it is, Korra had trouble with airbending because it was the element most opposite of her personality and because it would differentiate her from Aang. Thankfully she was able to master it by the second season, which was helpful since she had much bigger problems to tackle.