Without starting a fight, it just seems that you have great faith, not facts nor observation. Who says either was eating anything. Maybe they were just playing, like puppies, and (his, her?) tooth fell out in the fracas.
Let me ask you:
Do T. Rex dinosaur fossils hsve teeth or bones in their fossilized digestive tracts? Or is TR just hypothetically, and universally assumed, to be a carnivore? Or is it just unproven smoke and mirrors?
My suggestion: In God we trust; everybody else please bring data.
Occam's razor states that the explanation that requires the fewest assumptions is most probably correct-the simplest explanation IOW. A mouthful of exceptionally large, sharp pointed serrated shedable teeth most simply describes an animal that kills other animals and then eats them or that finds them dead and then eats them or both. In today's animal kingdom, we need only look at the great white shark to gain an idea as to the dietary habits of the T. rex. The great white shark is a modern apex predator that will also not decline to eat carrion should the opportunity to do so arise.
Furthermore, fossilized duckbill bones have been found in fossilized T. rex scat.
Check out considertheprobabilities.com and let me know what you think about it.