Programming is quite a remarkable activity:
- It has an extremely low barrier to entry
- You don't need expensive equipment
- You don't need to be in a particular location
- You don't need special credentials
- You can finding information / resources just by opening the internet
- You can learn it / do it independently
- It gives you rapid feedback (which can lead to rapid growth)
- It gives you frequent rewards (which gives a huge boost in motivation)
- It's objective and unforgiving (this is a good thing, because it teaches you how to confront reality)
- It's intellectually stimulating
- It's useful in the real world
- Corollary: you can make money or even build a career out of it
- It's badass (or are you telling me that Hackers WASN'T your favorite movie of all time?)
- Electronics (but this is basically still programming)
- Math (lacks "rapid feedback" and "frequent rewards"; "useful in the real world" is also questionable)
- Go, poker, video games (usually lacks "useful in the real world", sometimes lacks "badass")
- Juggling, poi (lacks "intellectually stimulating" and "useful in the real world")
So if you're doing simple math problems a hundred times a minute, your brain is doing lots of math.
This is part of what you don't seem to be getting. Repeatedly doing the exact same piece of extremely simple arithmetic doesn't require being good at math unless your definition of being "good at math" is at best highly non-standard. The ability to repeatedly count the exact same thing doesn't make one good at math and isn't even seriously indicative of it. That's aside from the fact that even if one did buy into this, this still doesn't address the fact that empirically there are people who by any sane notion of "good at math" are are terrible at music and people who have the reverse. This is one of many objections to your position that you seem intent on avoiding answering.