That is an anti catholic lie repeated by those who should know better. The few reports of cat killing were sporadic, not general, and do not fit the time line.
The plague epidemic was also killing a lot of folks in Muslim lands, Hindu India and in China.
The main witch craze was after the reformation so could not have caused the black death to spread 200 years earlier.
Finally, Rats are also hunted by barnowls, snakes and dogs.
They thrive in garbage, and medieval cities were like third world cities today, but worse because of horse manure was there too.