Humans made numerous mistakes through out the years. Either through pure ignorance, believing that they knew better, or they tried to play god and everything blew up in their face.
The creation of werewolves came exactly from one event such as these. Humans played around with chemicals that were better left alone. They had done it with the belief that they could alter certain genetic parts of humans in order to enhance natural abilities such as healing, strength, the six senses among other things.
When it didn't work out the way they wanted to and it was deemed too dangerous- scientists threw everything away in flowing water that ran not too far away from the lab.
Little thought was given about what might happen if animals came into contact with the chemicals that were mixed with human genes and other substances.
This was how werewolves came to exist.