There is no single 1 correct way to learn music
This is a subject that I have reflected on a lot. There's no single formula for teaching because there is no single formula for learning. While I absolutely believe in methods, the avenues in how they arrive are completely up in the air and vary widely.
I was lucky as a kid because in our house we always had instruments around. There was a piano in the living room and my dad's Martin acoustic guitar in the closet. When I was about 10, my parents surprised me with one of those Jr. drum kits. So there were always options available in the music department.
In fact, some of my earliest memories are playing piano with my older sister...mostly Chopsticks and Heart & Soul over and over again. Or just noodling around on the piano or guitar by myself trying to mimic melodies I heard on the radio or tv...pop songs, commercial jingles, tv theme songs, whatever. I was all about mimicking sounds that caught my ear.
The reason I mention this is because I learned music almost entirely by ear. I knew what the notes meant on the staff from some piano lessons, but wasn't great at reading it and honestly really struggled with it. On the other hand, if I heard a melody, I could lock that up in my memory bank forever. This came in really handy during my teen years when I started pursuing the drums more intensely. It was the mimic game again, but now with bands and drummers I really liked. I credit this time as the most foundational and still my preferred way to learn songs.
Since teaching however, I realized quickly how abundantly clear not everyone learns this way. In fact, it's one of the first conversations I have with new students so we can speak the same language. I think of it broadly in 5 ways: Visual, Auditory, Reading/Writing, Kinesthetic, and most important a combination of the 4. Everyone really is a secret sauce of the 4.
The nice thing is there are methods for all these ways of learning, and they can all create success. I have spent the last few years really digging into each style and method to be a more effective educator. And not surprising, it has improved my own playing quite a lot. I'm happy to say I fully embrace written notation these days and make sure at least the basics are understood by everyone I teach. Also it's hard to downplay how YouTube completely changed access to drum videos, past and current (I still remember the days of renting VHS tapes). So the wealth of having high quality visuals to learn from is priceless and something I totally rely on as well. My goto will always be the tried and true, put the song and headphones and listen. I just back it up now with adding other sources, very cool.
- closing thought -
Everyone has their strengths and weaknesses when it comes to learning. Make use of what works for you to your benefit, but at least try some other methods as well. Every additional tool is a net positive and you may be surprised how much your playing evolves by taking a different approach.