You can code. The whole point the article is trying to get across is that a lot of people are simply unable to learn how to code. You've learnt. You CAN become a professional.
You just don't realize it.
The step you've taken is the hard one. In fact, there's another big dirty secret in programming.
A load of professional programmers aren't able to do what you can do, they can't make new programs. They can only modify existing programs. Making new programs is beyond them (or at least takes them an inordinate amount of time). Automating scripts to make their job easier is something that they would take weeks to do.
EDIT: I'm not sure I agree with the article though, I've heard several arguments that we simply teach programming badly. Especially in universities.