A couple of thoughts.
Art is that which is made for its own sake. I find this definition compelling.
Art is also about beauty—genuinely so. There is a real distinction between self-expression and beauty, and confusing the two muddies the conversation. Not everything that expresses something is art, and not everything expressive is beautiful.
The clearest image I have for this is the crucifix. Probably the most painted, drawn, and sculpted image in history, the crucifix is transformed by art from a grotesque instrument of torture into something that can even become modern jewelry. That transformation is astonishing. I cannot think of a true counterexample—something that is genuinely art and yet not beautiful in some way.
Yes, images can depict ugly things or tell horrific stories. But when that happens, the image often functions primarily as storytelling rather than art as such. If a terrible scene transcends mere narrative and becomes art, I think what we are responding to is still beauty—perhaps a severe or tragic beauty—but beauty nonetheless, even when the subject matter is horrifying.
This distinction is important because it allows us to exclude propaganda and advertisements from art. They may be visually clever or emotionally manipulative, but they are made for a purpose beyond themselves. Their end is persuasion, not beauty.
So: art is that which is made with beauty as its center and is made for its own sake—not as a means to something else.
Consider stained glass windows. They are functional, yes, but the argument still holds. The window could have been merely a window. The art is the stained glass image itself. It does not depend on being a window to be art. The same piece could be mounted in a light box in a museum—as so many are—and nothing essential would be lost. The window serves a function; the art does not. The art exists for its own sake.