Does art have to tell a story?

Continuing my exploration into So, why is this art? I will examine the second of the key points:
Does art have to tell a story?
The Contemporary explores this question thusly:

For centuries, philosophers and artists believed that art must tell a story or have important meaning. In order to fully appreciate the artwork, viewers had to "read" this story from the image and understand its meaning.

...many people still believe that art should express some great idea of tell a story. Therefore, to fully appreciate and understand a work of art, viewers must understand the message behind the work.

This concern for meaning in art expanded in the mid-1800s... As the messages became less obvious, viewers were challenged to decipher a story or understand the meaning of the work.

A lot of people do still want to see some kind of narrative in art. They want to be able to say that they "get it" and to feel that they understand the meaning conveyed. They want to feel as though they are part of the discourse. Art is an amazing tool for communication and I typically approach it in this manner myself, but I do not think that the communication need be so obvious that the casual observer can fully appreciate it and move on. Many viewers like to be challenged but still to "get it", as if they are let in on a secret that not everyone is privy to. It is good to have a range, and not all meanings should be easy to access just as not all meanings should be hidden. There are many kinds of art and many kinds of artists, and it is in this diversity that we are able to better understand and appreciate one another and consequently ourselves.

And some artworks that may not have an apparent message or obviously tell a story do actually still follow a narrative all their own. Many artists develop into their styles over the course of their artistic careers and, with a little research, it becomes much easier to see the ongoing narrative from one piece to the next and to see how the artist was shaped and influenced through past works to what they are creating in the present. This type of narrative does require extra work on behalf of the observer but can lend to a far greater appreciation in the long run than just being able to look at something with which he/she had been previously unfamiliar and "get it". Being able to follow the artist's career over time, the choices made, moods conveyed, artistic explorations and maturity into and out of particular styles, can be a far more genuine and telling narrative and can offer an even better glimpse into the artist's soul, likes and dislikes, struggles and sense of self.