No, but I've encountered similar false equivalences/appeals to emotion/guilt trips made, such as calling meat eaters "murderers", or comparing meat-eating to human slavery.
As someone who shares much of the animal empathy that causes people to become vegetarian or vegan, AND who opposes factory farming, such reasoning can hardly be called reasonable. In addition to being filled with logical fallacies, it's classist, since it doesn't take into account the fact that vegan diets (in particular) are VERY expensive in terms of getting the proper nutrients; it's ableist, since it doesn't take into account the various health issues people might have that would make a vegan diet dangerous for them, and never seems to address the fact that domesticated cats and dogs are largely carnivorous and require meat to survive.
Empathy is about feeling the emotions or pain we perceive in others. Extending that to non-human animals isn't really that hard, or even always unreasonable. Many animals do have humanlike sentience. I'm willing to work away from eating pork or octopus, for example. But other animals that we eat, such as cows and chicken, don't demonstrate that degree of sentience to my knowledge. And ESPECIALLY when it comes to fish?! It's been scientifically verified that fish can't feel pain, so as long as they're not endangered, chow down on that sushi.
I'm okay with working towards a world where vegetarian and vegan diets weren't so expensive, and factory farming no longer happened, if nothing else for the sake of the environment. I hope that will be achieved soon with lab-grown meat that didn't come from a killed animal.
Empathy isn't always a good thing, as it can be misapplied and used to justify an elitist position.