I happen to think that a lot of people don't feel "emotions" when "viewing art" because the art that's obviously available is either totally irrelevant to your life (e.g. bourgeois portraits of rich people from the 1600s, vivid scenes from places you've never been, full of religious symbolism) or totally alienated in the special contemporary way (performance art, most of the random crap made by self-absorbed young artists, etc).
There's also a thick nearly opaque wall of posturing involved, so that talking about art is often an anxious display of cultural capital.
Learning to love art, like learning to love wine, is heavily tied up with class and the attempt to "understand" the acquired tastes of the upper middle class.
Staring at paintings in exhibition rooms or museums is also a very unnatural thing for a human being to do. Great art from the past wasn't made to be "exhibited" like that, it was usually part of a context, from which it was later extracted, or literally stolen.
You can think of a painting in terms of "how would this subtle affect my mood if I hung it on the east wall of my living room?" That's a function of art, too, and probably a more authentic and real one. A lot of art was made to hang in churches for inspiration, so if you're inspired by religion, that's a whole thing.
Maybe you'd like to try going to a museum of history and viewing some ancient everyday tools, coins, and jewelry. Those are things that were carried around by people or kept in their homes, and people wouldn't usually stand around staring at them and admiring them, so you're not experiencing them as they did, and there's no need to feel "emotion" in any romantic or dramatic sense... but those artifacts are still very interesting, beautiful, and provoking the imagination.
You can also be interested in paintings in this way. Go to an art museum, find a painting that seems interesting in some way, not necessarily because it overwhelms you with feelings, but maybe just because it seems odd, strange, or curious... Or you just don't understand it.
Then you can realize that a single painting, because it contains so much information in the whole tapestry of its context and history, is like a portal into another world that you can explore, if you want to... and that's kind of amazing.
I think the idea of a painting as a radiant artifact that makes people swoon with awe is pretty strange, and possibly only applies to people with a certain abnormal genetic kind of synaesthesia.
Van Gogh painted a lot of scenes from nature, because he loved nature, and walked a lot in the countryside. What I think is amazing about Van Gogh is that he paints those scenes not just as "beautiful" in a simple sense, but sometimes in a way that makes the landscape looks lonely, sad, or even distorted in a strangely vivid and almost scary way.
I doubt Van Gogh himself would say that his paintings "lived up" to the lived experience of being in the countryside during a sunset, say. But they mirror it in an interesting way, and having seen those paintings, one can see the countryside in a somewhat different way, or with more complex resonances.
His letters are fascinating to read. Some quotes:
“What I want to express, in both figure and landscape, isn’t anything sentimental or melancholy, but deep anguish. In short, I want to get to the point where people say of my work: that man feels deeply, that man feels keenly.”
“Many a worker in a factory or shop has had a strange, beautiful and pious youth. But city life sometimes removes ‘the early dew of the morning.’ Even so, the longing for ‘the old, old story’ remains. What is at the bottom of the heart stays at the bottom of the heart.”
“What am I in the eyes of most people – a nonentity or an eccentric or an obnoxious person – someone who has no position in society and never will have, in short the lowest of the low. Well, then – even if that were all absolutely true, I should one day like to show by my work what there is in the heart of such an eccentric, such a nobody.”
He's a very different person from me, but I found his paintings strangely interesting, and after reading the letters I find his whole life fascinating, and that gives me a bit of an entrance into being interested in the whole scene of the Impressionists in Paris where his style changed so interestingly, but also the "old Dutch masters" that he was emulating at first, like who were those people, what was going on there, what were they trying to show...