First, most writers (the real ones) are readers. If words are on a page, then the words must be read. Otherwise, how do they live? If they sit still on the page, left behind by the writer who abandoned them, there is no oxygen to them. This is something writers understand, so they will read the words.
Second, there is a certain level of competitiveness. We must make certain the words written by others are not inherently better than our own. I mean, do they (the person whose shoulder we're reading over) know the proper use of whose?
But mostly I think writers will read over your shoulder because of a distinct need to know. We're nosy. We want to know the inner-most workings of a brain.
We want to know what observation you're making about the world. Did we miss something?
We wonder what is so important to you that you need to get it on paper. We want to know what your handwriting looks like. We want to know how your type so fast that the words, these series of letters, appear so quickly and represent whole universes that didn't exist until now. Just now. As the ink spilled from your pen, bringing something of order to the chaos of space.