If you think it's because artists were always trying to hide Jesus' secret face tattoo, you should know that this phenomenon comes up in most paintings, and nobody was ever sure why. It turns out it's due to brain weirdness.
Sam Kean, author of The Tale of the Dueling Neurosurgeons, studied this weird phenomenon. He says that if the choice of which side to depict was totally random, we would find that gallery collections have roughly a third of all portraits facing straight forward, a third facing to the left, and a third facing to the right (obviously). However, studies show that this isn't the case -- about 60 percent of subjects sit with their left cheek facing the viewer, their left eye practically in the middle of the painting. It's twice as common as it should be.