What is Taurine
It helps muscle function, may aid athletic performance and endurance, helps reduce anxiety, and appears to aid blood sugar regulation and cardiac health. It's an organic molecule (not an amino acid) named for the Latin taurus, which means ox or bull because originally taurine was extracted from bull semen and ox bile.

No Bull
Although there is taurine in bull semen, this is not the source of the ingredient in Red Bull or other products that contain the molecule, such as baby formula and cosmetics.

Taurine is found in other animal tissues including the human intestine, breast milk, meat, and fish. However, chemical processes can make taurine from other source molecules in much the same way your body does. Specifically, taurine may be synthesized by reacting aziridine with sulfurous acid or from a series of reactions starting with ethylene oxide and sodium bisulfite.

So Jack the most likey source of your backwards theory probably comes from the attempt to spend the least by the dog food manufacturer and their marketing dept.