system
Given the following post, respond as if you're commenting on Reddit:
human
[Avatar The Last airbender& Korra] metalbending avatars

When Korra was in Zaofu, she learned metalbending from Su and she congratulated her as being the first metalbending avatar but why didn't Aang learn from Toph in the years he was in Republic City. Toph knew metalbending and also had an academy for that so why did Aang not learn it.
gpt
The two biggest reasons are likely that Aaang couldn't metalbend and Aang didn't have the time to learn to metalbend. 
 
Aang doesn't seem like a metalbender, he already heavily struggled with learning Earthbending as it is. His more airbender personality doesn't suit itself to metal and we know that personality and temperament has an enormous effect on learning bending and disciplines of bending. Korra on the other hand has a natural stubborn metalbender personality which is why she picked it up naturally.

The other reason is that Aang didn't have the time to explore the sub disciplines of bending at his leisure. For all that Aang is deeply spiritual and more suited to learning, study and meditation, his time as Avatar was marked with a heavy focus on the material world. Between reintegrating the Fire Nation, restoring balance and peace, founding Republic City, rebuilding the Air Nation temples and Air Nation culture and in general fixing up the world after 100 years of war, Aang didn't have the free time to master other bending arts.