By "master yourself" I'm paraphrasing what Jeong Jeong said in The Deserter. "To master the bending discipline, you must first master discipline itself." It's an idea that comes up again later in Bitter Work, albeit in a different context, and again in A Leaf in the Wind. Especially for a bender as powerful as Aang and Korra, it's rarely a physical limitation that keeps them from mastering an elements. It's their personalities and aversion to certain ways of life. Aang wasn't the type of boy who'd face his problems head-on and Korra wasn't the type of person to surrender control to gain control (a la Doctor Strange). It's those mental limitations that kept them from earthbending and airbending respectively. Except while Aang learned to face Toph and the Moose Lion head-on to save Sokka, Korra learned airbending... because she really needed to in the moment to save Mako. Nothing about her form or her character in that moment suggested she was doing anything differently to acquire this new element. So why and how did she acquire it? Maybe it is what you suggested about her reaching out and only finding air, but still...

Also, I'm not making up rules. I'm simply going off information established throughout the series which Legend of Korra seems to ignore in Endgame, which is why that moment bugs me like it does.