Programming is part craft, part science, and occasionally a very small dash of inspiration or art.
But for the most part I think that a very large amount of it is very comparable to bricklaying. Especially in the part where most people in the IT world make their money, such as software for the financial and the business world.
Rarely does it elevate itself to the level of watchmaking and even rarer do you find art. It does happen though, but not often.
I'm sure that programming is conceptually different from bricklaying in a sense that we are solving puzzles, sometimes. But everybody that got in to it for that reason knows that the only time you really need that skill is when you've messed up and you are facing a very tough bug.
Once you get better at programming it is more like knitting or weaving than puzzling.
Of course there are different styles of programming, and there are only so many kinds of brick. But programming for the most part is hard because we have chosen to make it hard. If bricklayers had to create each and every brick from clay and bits of stone then you'd be much closer to what programmers do for a living than what bricklayers do.
Bricklaying has been 'industrialized', and one day programming will be too. It will probably still be marginally harder than bricklaying, even after that has happened. But if you can explain what you want done and in which order then you are essentially programming.
People often say they would like to learn how to program but they are not smart enough for it. And plenty of programmers just love that because it makes them appear special.
But I think anybody can program, the difference is not some binary switch in your head 'programmer/non-programmer'. The difference is in how complex an arrangement you can create, and that's a continuum.
Some programmers are better at this than others and can solve more complex problems.