That is a double edge sword. It would be great for current pet owners who want to provide adequate care. I have seen the costs with pet ownership of different animals, and was friends with vets. They have seen animals put to sleep simply because the cost of treatment was too high for the owner to be able to provide that care. Being able to regain some of that cost in the form of a tax break may have saved the animal's life. I have some concerns as well. How many people will get a pet thinking they can get a tax break, when in reality the amount you can write off on your taxes is less than what the cost of the animal is? It's like when people call kids their tax write-off. This is said in jest, but some people may actually see animals in that way. Just like anything else, you can't legislate intelligence and responsibility.
What if people start adopting animals just to get the tax break and neglect the animals? It would be a good way to promote pet ownership, but it's inevitable that some animals would not benefit from this.