A division into herbivore and carnivore is somewhat artificial. There is of course the category of omnivores, species that eat both meat and plants, also featuring a number of primates --- that hunt in packs, just like early humans used to.

Meat eating isn't something that humans have recently invented, meat has been an important source of human nutrition since early prehistoric times. The amount of vegetables in our diet has only increased with the dawn of agriculture within the last 10,000 years.

Humans see more have known the use of fire and have used it to cook their food since days predating the rise of Homo Sapiens. Incidentally we also cook and season the bulk of the vegetables we eat. Raw potato, anyone?

As far as cultivating compassion etc. goes, every emotion is integrally tied with our perception of the world; and as much as perceptions vary, the applications of subjective emotions do. A believer in plant sentience would rather see an animal harmed if it were necessary for nutrition.

There is also a whole other body of considerations when it comes to direct and indirect violence. If you don't eat locally grown organic vegetables and fruits, the amount of violence associated in the planting, harvesting and delivery process is unbelievable.

For example, you could rephrase the question: "For every breadroll you eat, insects and mice will be killed by poisons and in the jaws of huge machines. Do you really want to eat that bread?"

If someone wants to be an ahimsa (non-violence) absolutist, I suggest you study Jainism and their solutions. They have pretty much taken it as far as it goes.