Pets can be either domestic or wild animals. Domestic animals like dogs and cats prefer human company while others, like canaries and guinea pigs, cannot survive without being looked after or protected by humans.
Wild animals kept as pets generally have to be kept caged to prevent them from escaping.
Domestic animals often give their owners a great deal of comfort and joy and usually receive it in return. Wild animals, on the other hand, almost certainly prefer their natural environment and the company of their own kind.
Some people keep unusual or dangerous wild animals like large spiders, reptiles or even great apes, not to receive or give affection, but to enhance their ego and make themselves appear more interesting than they really are.
A responsible Buddhist would probably not want to contribute to this problem.