Why Do We Pay Tax For Pet Food, But No Tax On Our Food?

food is considered a necessity
having pets is not a necessity and therefore their food, upkeep, vet bills etc is a personal thing
animal control is a very prominent program in many cities that have an overabundance of animals,
even some legislation has been suggested to limit even pure bred animals

Actually, in many states, you pay taxes for the service of preparing food, while the “product” of the food is not taxed if it is incomplete. That means that if you bought a microwavable hot dog at the grocery store and left the store, you would not pay taxes on it. You could take it home, put ketchup, mustard and relish on it, and now you’ve finished preparing it.
At many restaurants, if the food is hot, or if you eat it at the restaurant, they are required by the state to charge you taxes on the meal because the preparation was a “service”. (That’s one of the reasons they always used to ask “Is this for here, or to go?”)
Dogs, not having thumbs, are completely unable to prepare their own food. That makes their food a “finished product”. Yes, the tax laws seem pretty obscure, but the government comes up with justification for everything. Maybe you could start an argument in your state legislature – something like “I put gravy on my dog’s kibble!” It isn’t a completed product! I don’t think they’ll listen though, because most states are hurting for taxes about now.

Because your state decided that you would pay tax on it.
BTW, not all states exempt human food from sales taxes! MO has a lower rate (1.225% vs 4.225%) for food for off-premises consumption but most local option rates apply across the board so a 4% or higher rate on food is common in most of MO.