There was a story on the news recently about a woman who was attacked by her friend's pet chimp... who ended up tearing her face and hands off. O_o Chimps should never be kept as pets; they are wild animals.
Chimpanzees can never be trained fully to hold no risk whatsoever of hurting their owners. Especially since people who have them as pets very rarely see them as being wild animals; more like hairy people. Other primates are kept as pets, but chimps are more dangerous than, say, macque monkeys, cuz of their immense strength. They are far stronger than humans, and are never fully tame, no matter what their owners may think; there is always that risk that they may turn on them. Males are particularly aggressive.
Dogs and cats have been domesticated for thousands of years so the risk of horrendous injury from them is very small if the animals are trained correctly. However, all the training in the world can't take away the chance that your pet chimp Billy could one day take offence to your habit of patting his head and rip your hand off, before pelting you with faeces and ripping your eyes out of your skull.
Also, chimps and other primates who are destined to become pets are taken from their mothers at a very early age. You can only imagine the trauma that they go thru. Also, while baby chimps may be cute and cuddly, adult chimps are not. An adult male chimp is ten times stronger than a human, and very capable of throwing massive tantrums which could see you heading into an early grave... in pieces.
Hell, even trained professionals who keep them have to put in place all kinds of security measures to ensure that their charges do not escape and wreak havoc. The fact is, a chimpanzee is a wild animal. No amount of putting them in clothes, feeding them cake or letting them sleep in your bed can change that fact.
Why would a chimpanzee attack a human?: Scientific American