Should the law restrict what animals can be kept as pets?

I think it is important to define what a "pet" actually is. To some people, a pet can be any creature that they have in captivity, whether that creature is happy to be there or not.
Others of us, including me, believe that a pet is an animal that we keep, care for, and the animal enjoys our company as much as we enjoy their company.
Looking at the first definition, a person can keep a spider, snake, fish, or just about any kind of living creature and call it a pet.
But, that does not truly make it a pet. If a true pet is one that enjoys living along with human beings, then we will be eliminating many of the animals, reptiles, and bugs, that we have discussed in this topic, as well as most of the wild creatures who are also sometimes kept as a pet.
Truthfully, those creatures might more aptly called a hobby, or even a curiousity, rather than a pet, which they definitely are not.