Responsible animal owners deserve at least as much protection under the law as do responsible drivers of cars. Responsible users of cars are not punished for what drunk drivers do even though over 47,000 people are killed in automobile accidents each year.
Equal protection under the law is a bit more than treating all animal owners equally. It also includes rewarding citizens equally for equally responsible behavior. Automobile drivers who do their daily driving safely are rewarded by being allowed almost unfettered access to the highway and very lax requirements for renewing a license. The state actually facilitates access to the highway and the obtaining of a license.
Punishing every owner of a pitbull or a monkey or a tiger for something that went wrong somewhere else with someone else's animals is denying them the kind of legal protection that every owner of an automobile enjoys. When a drunk kills an innocent family of four, the authorities don't go out and ban everyone else from driving a car. Far from it, they actually take steps to make other drivers safer. They protect responsible drivers from irresponsible drivers, rather aggressively.
The keeping of animals is just as much a necessity as is driving a car. For physical well-being, we need our food animals and it has been shown that pet owners are healthier, more resistant to disease and less likely to die of heart attacks and strokes. Most animal species have proven to be good for human emotional well-being. Emotional well-being is a necessity.
No one has yet shown that an escaped exotic pet has killed anyone in the United States in its entire history. All deaths due to exotic pet attacks in the entire United States add up to a statistically insignificant number. Rexano's website has several articles about the safety of keeping non-traditional pet animals. Not only does it seem that less than one person per year is killed by big cats in the U.S. but it also seems true that pets are less likely to kill than those handled by "trained experts." Either way, even if it were justifiable to restrict a right due to actual deaths related to the exercise of that right, this isn't one that has been shown to be very hazardous.
By the doctrine of equal protection under the law, a less hazardous activity should be subject to less control and scrutiny than an activity that is more hazardous, and that control and scrutiny should be the least necessary to achieve a valid goal. Drivers of cars and riders of horses are not subject to any formal training requirements at all. People are killed about every other day in the U.S. by horses and no one anywhere has to pass a test to own or ride a horse. To drive a car a person has only to pass a written test and a driving test. It is wrong to the point of being unconstitutional to force people who want to own tigers to fulfill requirements that are more stringent than those imposed on drivers of automobiles.