The animal rights organisation said using animal names as slurs "isn't just harmful, but also inaccurate".
"Pigs, for instance, are intelligent, lead complex social lives, and show empathy for other pigs in distress. Snakes are clever, have family relationships, and prefer to associate with their relatives," Peta said.
"Anti-animal slurs degrade animals by applying negative human traits to certain species.
"Perpetuating the idea that animals are sly, dirty, or heartless desensitises the public and normalises violence against other animals."
While offering optional insults, Peta did remind people to "always be kind and consider not using insults at all".
"Peta urges everyone who believes in equality and justice to take a look at their personal beliefs and the language they use, and break free of this outdated mindset that denigrates other animals," they said.
The latest idea from Peta has been roasted online, with thousands of people piling on the organisation's tweet.
Controversial Republican Senator Ted Cruz labelled the idea "bullsh*t" while author Michelle Elman brought up a previous animal insult Peta itself had used.
Author Mark Dice said Peta's latest campaign cemented the group as a "parody".
"Peta is a parody of an animal rights group. They must be," he wrote.
"Your name is offensive to pets because it reinforces the myth that all pets are ludicrously woke imbeciles," columnist Piers Morgan added.
Others who supported Peta even called out their latest tweet.
Peta is not backing down on its call to change the insults, even calling on dictionary companies Merriam-Webster and Dictionary.com to update their definitions.
"Peta is calling on Merriam Webster, Dictionary.com and others to help combat speciesism and reduce animal abuse by removing derogatory definitions of pigs, snakes, and dogs," the organisation wrote.
In two particular examples, dog is defined as a "despicable man or youth" and a pig as a "dirty, gluttonous or repulsive person".
