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")
This appears to me to be a highly nonstandard use of the word "counting".
They most certainly can. Counting to 12 is a teeny tiny weeny itsy bitsy fraction of mathematics. You can be very good at counting to 12 and terrible at mathematics overall.
It seems more as if the issue is that you think arithmetic is all there is to mathematics. I'm sure you don't actually think that, because it's silly, but I don't see how to make any sense of what you're saying without an assumption along those lines.