In my opinion, first you need to have the drive to want to learn and a questioning mind, which it seems that you have. To a degree it will depend on how much info you are able to gain in person where you live. I my case I am fortunate to live around a large metro area which has enabled me access over the years to in person classes and lectures by several avian vets. I have completed courses in aviculture that span a wide variety of subjects and have done a lot of reading of medical related info. By far the biggest asset in all of it is being able to discuss in depth, any issue with my team of avian vets, whether it is an issue I am experiencing with my own flock or not. A lot is gained by personal experience, when I have an ill bird the goes to the vet I want an in depth explanation for example, don't just tell me there is a GI infection, I want to know how it is contracted, what exactly it is, how it was determined and an explanation of the test results in detail, what is going to be used to treat it and why that particular drug was chosen etc. You may want to watch this to give you an idea of what it takes to become an avian vet.
video about what it takes to become an avian vet