Syntinen Laulu is right, what Hamzah said has been badly misinterpreted by the press.
The idea that veganism would drive out such phrases just doesn’t square with how language works. Metaphors hang on long after their literal sense is no longer understood or applicable (e.g., dead as a doornail; dial the number, tape the conversation). Such phrases may eventually fade away, but if so, it would not be because we changed our eating habits or the way we treat animals. But that’s not the focus of her article. When she writes about the future use of such animal metaphors, she’s mainly talking about the production of new metaphors, and that’s absolutely right. As we grow more aware of the sentient nature of animals, metaphors based in cruelty or consumption of animals will become less and less likely to be created. The old metaphors will hang on, as Hamzah states.
Also underlying the idea that they can be made to disappear is the belief in the strong sense of the Sapir-Whorf hypothesis, that the way we speak influences how we think. If we no longer talk about mistreating or eating animals, then it will quite literally become unthinkable and such actions will stop. (Nothing in what Hamzah says indicates she buys into this, but PETA certainly does.)