Before you can say why most art seems boring, you need to say what “boring” means.
There are three basic kinds of boredom.
Boredom is often associated with experiences that make us anxious. It’s boring to wait for 45 minutes in a doctor’s office, while sitting on a moving train for the same length of time can seem like an interval of freedom–an opportunity to read or daydream. Boredom is also associated with unfamiliarity. As another answer points out, it can be boring listening to people speak a foreign language. You feel like you ought to understand what they’re saying, but you don’t. (This leads back to anxiety-as-boredom.) Paradoxically, boredom can also result from excessive familiarity: when you hear or see the same thing over and over, you get frustrated by the lack of novelty.
Art can fall prey to all three kinds of boredom.
Some people are bored by the Old Masters in the Metropolitan Museum of Art, because the Met seems like a temple dedicated to wealth and privilege, and they feel excluded. Conversely, some people are bored by the contemporary art at PS 1, because it’s so relentlessly hip and disdainful of bourgeois values.
Some people are bored by Baroque altarpieces or Chinese scroll paintings, because their formal qualities are complicated and their symbolism is obscure. They are the visual equivalents of foreign languages. Once you achieve even a basic understanding, there’s a big payoff, but it requires a lot of work–more than looking at, say, Michelangelo or Matisse.
Finally, there’s a vast quantity of second- or third-rate art that is boring if you know the first-rate art it derives from. A lot of modern art, or instance, is really just a riff on Matisse or Picasso. It’s like listening to top-40 radio, where most of the songs are re-makes of other, better songs. They’re OK as background music but boring (indeed irritating) if you pay attention.