Curtains Won't Close All The Way?

I have a set of curtain rods that will not meet in the center. There seems to be something holding one of them back. Most of the time I don't use the cords, just pull them open in the morning, and pull them closed at night and pull the fabric together and clothespin it to provide privacy. I don't use the cords much because the cats eat them and I have them safely put up. There is enough play in the cords to stretch the whole way across the window, so this is not what is holding them back. Any Ideas?