The discussion happened on Good Morning Britain today where the charity's media officer Jennifer White from Edinburgh was grilled by Piers Morgan on the point.
Arguing PETA's case, Jennifer said: "A lot of people at home who have dogs and cats refer to them as pets and they refer to themselves as owners, and this implies that the animals are a possession.
"We don't hate the word pet - we're encouraging people to use a better one."
He then proceeded to criticise the list of of animal related phrases that PETA want to ban given their potential harmful meaning.
Some of the examples in its website include: Kill two birds with one stone becomes feed two birds with one scone; let the cat out the bag becomes spill the beans; hold your horses becomes hold the phone; put all your eggs in one basket becomes put all your berries in one bowl.
Viewers took to social media to share their opinions on the debate.
One viewer agreed with Piers saying: "For once, I actually agree with @piersmorgan. Not being allowed to call your pets a pet is absolutely ridiculous #GMB."
Another felt sorry for Ms White and said: "Oh dear that poor young woman on #GMB . Eaten alive by Piers and the dog owner! She has definitely let the ‘cat out of the bag’!"