Werewolves exist, but not in the form portrayed in the media. The media image portrays a change in form under the influence of a full moon, and this all quite out of the control of the human infected by a bite. A dramatization of the real situation, which happens rarely and is indeed an infection, the result of a bite - rabies.
What happened in the past when a rabid animal, most often a wolf, tangled with and bit a human. Wolves normally avoid human contact, but when wildly irritable with an infected brain, they savage anything that disturbs them. The infected human first finds insidious changes setting in - irritability, snapishness. During the course of the disease the afflicted human would become unkempt - hair and nails growing long. And in the final stages of the disease, madness and extreme irritability set in - the man having become the wolf. Why does the legend tie the madness to the full moon? Even unaffected humans grow a bit wild during the full moon, but a human in the final stages of rabies, wild eyed and howling with pain, snarling at all who come near, would be more noticeably affected. The full moon become the point where it was all too much, and quiet suffering became anguished howls. Tormented in the villages, rabid victims often sought the quiet of the woods to soothe their hyper-irritable nerves. Thus, the legend.