While in theory any animal might be a pet, in habitude only a inconsequential prime of species of mammals (especially dogs and cats) and other small animals, such as birds, fish, or lizards, are practical. Separate induction for this is that large fish are not able to fit inside humble dwellings.
In general, a pet must either be inconsequential enough (or easily controlled) for his or her undesirable behavioral tendencies to be negligible, or the brute must be in reality domesticable