One charitable interpretation is "it's something you learn by doing, not something you learn by reading".

"Art" has a bit of a double meaning, there's the "something that's pretty/pleasing/aesthetic/original/creative", but there's also the "craft" meaning, as in "the art of XXX".

I want to focus on the "art is inherently intuitive and not about breaking things down into components like science" part. My thought is that these people who say this are confusing their map for the territory. They may not know how to deduce what the perfect painting would look like, but that doesn't mean that it's not possible.

Two reactions to this:

1) If someone says something can't be broken into component parts, a more charitable reading is that they think that trying to do so is a waste of time and less likely to bring progress than just a lot of practice. Even if it's possible in theory, that doesn't mean it's actually a good idea, so warning people against it can be totally reasonable, and isn't "confusing their map for the territory".

2) HOWEVER, in the case of art, most forms of art I can think of - drawing, painting, storytelling, animations, etc. - most definitely CAN be broken into component pieces, and often those component pieces can be broken into component pieces too, etc. - just check out the right section in any library.

You can't learn to draw by reading a book, but a good book on drawing can tell you what individual skills you should practice, and how to do so.