Ok, so these two things don't seem to have a connection, but they do.
When the Pope said that cats were diabolical in 1232, he caused an increasing amount of anti-cat sentiments with time.
Cats were loud and noisy at night, causing many people to become superstitious about them and associate them with the devil.
Cats and even their owners began to be executed in large numbers. Cats and owners alike were accused of witchcraft. During the next 100 years, cats were slain in great quantities.
Killing off all the cats ended up killing the rat's predator, and rats carried the bubonic plague. When the plague began, there weren't many cats to kill the rats running around everywhere.
Between 1347 and 1352, a third of Europe's population died of the bubonic plague.
The rats ran rampant in Europe and reproduced exponentially and quickly. With no cats to prey upon them, they continued to carry and spread the deadly bubonic plague.