Korra suddenly airbending out of nowhere when Mako was about to lose his bending had zero foreshadowing, and zero post-fact explanation in the show. Even the creators' Word-of-God explanation of her unlocking her Air Chakra doesn't make sense because the Air Chakra is blocked by grief, and Korra didn't suffer from grief at all during Season 1, let alone overcome it.

It happened because the plot demanded that it happen, no other reason. 

Seriously, this moment is why I will stand by TLOK Book 1 being worse than TLOK Book 2; all that buildup and then it absolutely crashes and burns when it tries to bring it all together.

A much better outcome would have been if she had learned airbending earlier, Amon takes her bending, and then she enters the Avatar State to beat him when he's about to take Mako's bending. This is better in literally every way:

1. An Avatar uncontrollably entering the Avatar State when their friends are in danger was established back in ATLA, so her being taken over the the Avatar State to beat Amon & save Mako wouldn't feel like it came out of nowhere like her Airbending does.
2. The Aang flashbacks literally show that the Avatar State is the key to overpowering a bloodbender. Aang's airbending is pretty useless against Yakone, yet somehow Korra's far less experienced airbending is Amon's Kryptonite. The Aang flashbacks should have been foreshadowing how Korra would defeat Amon, but nope. Bryke gave themselves the perfect set up and then completely ignored it.

13 years later, and this is still the worst written moment in the franchise.