There is an idea that is being explored by the scientific community that meat could be grown from a single cell which is duplicated enough times to make an entire slab of muscle tissue without a large amount ever having to be taken from a complete animal. You can read up on it a little here:
http://en.wikipedia.org/wiki/In_vitro_meat
Because no animal is harmed in the process of making this product, this is most likely the solution to the idea of how to ethically be able to feed meat to humans or especially, PETS.
Cats could be raised on a diet of pure meat (which is what they really need to be healthy) and no animal would ever need to be harmed (aside from one original cell taken from the muscle tissue of one cow, which is basically like a mosquito bite to the cow.)
Dogs and other animals could have meat, and even humans who refuse to give up meat could eat it to their heart's content (no pun intended) with no animal's deaths on our conscience.
This technology can also be used to make eggs and milk products without need for a chicken or cow at all.
