In Dwarf Fortress, cats will adopt dwarves without those dwarves needing to do anything. If cats which have been adopted by dwarves are slaughtered, the dwarf will have a tantrum. Tantruming dwarves can do bad things - so you want to avoid that.
However, once the population of cats reaches a critical level (which is quite fast, because cats are promiscuous and have large litters of kittens) it becomes impossible to curb and keeping track of so many moving creatures causes the game's framerate to spiral downward rapidly into unplayability. This is known as a "catsplosion".
The best way to stave off a catsplosion is to slaughter all your kittens. Not very nice but you could make roats and leather out of them.
Forums at GameFAQs