I watched the episodes again on their broadcast premiere yesterday, and I noticed something about episode 2 that I missed the first two times. I realized that Mako and Bolin were essentially showing Korra the same thing that Tenzin was trying to teach her with the spinning paddle thingy, how to dodge and evade. First when Mako was doing the rope-a-dope move, "bobbing and weaving" to dodge the attacks and save his energy before striking back, then when Bolin told her how she had to keep her stance loose and mobile so she wouldn't be a sitting turtle-duck (or whatever). It was the same principle as the airbender style, a focus on evasion and redirection. But when Tenzin tried to teach her that, she resisted because it was couched in the Air Nomad culture and philosophy that she found alien, and so she didn't see it as something she could understand or internalize. But pro-bending is a competitive, aggressive sport, and that's a mindset she can readily relate to. So when she saw that the same principles of giving way and evading could be an integral part of competition, that's what enabled her to accept and understand Tenzin's lessons.
But that was worked into the story so subtly that I didn't realize what was going on. I'd figured it was just the urgency of the situation, when she was on the verge of losing, that forced her to focus and start using what she'd learned. Now I see there was more to it, and it was very cleverly and subtly seeded throughout the pro-bending scenes. That's really impressive writing. Gotta love those layers.