But if you're talking about really learn how to program, for example to learn the skills necessary to create a basic blog with a database, login, posting, commenting, etc. Then, no, not everybody can do that. If you get some experience in the real world and try talking to people who aren't technical, it will become readily obvious that not everybody can do it.
It's not that programmers are "a special breed", stop being so coder-centric. There's plenty of things you're not good at and can't do as well. Or do you believe what we were told as children; you can do anything! Sorry, but you can't.
You'll never be a Formula 1 driver. You'll never be a fighter pilot. You'll never play in an international level orchestra. You'll never be an architect or civil engineer. Et cetera.
And billions of people will never be programmers.
It's not that programming is so intrinsically special, it's that it's one thing among many things people have varied proficiency for (the origins of that proficiency I have no idea and won't get into), and some have no proficiency for whatsoever.
This is all really obvious if you've spent much time with people who aren't programmers.