As you might imagine, people find it ridiculous to consider a tax deduction for pets, despite the fat that nearly 70% of Americans "own" pets and that mountains of research delineate the many positive consequences of living with and interacting with non-human animal companions.
One argument is that pets are "optional." Well, so are children, yet people think nothing of getting special deductions for them. Another relies on the illogic of descent-- tax breaks for pets will lead to tax breaks for houseplants and who knows what else. Simply ridiculous.
I see such legislation as a move toward citizenship status for non-human animals. And this is exactly why, consciously or not, people are opposed to the idea. For Americans and most of the world, animals are not citizens and not worthy of any legal benefits. While the HAPPY Act would not directly provide citizenship benefits to animals, it could encourage more responsible pet stewardship which could indirectly serve to increase the status of non-humans.
Here is the original bill.