Language is, without doubt, becoming more and more politically correct and so we now hesitate to use the term ‘owner’, despite that pets are legally considered chattels (personal posessions) in UK law.
I have conditioned myself to use the term ‘pet parent’ because, after 49 sits, it’s probably the least potentially offensive. Personally, I dislike the terms ‘furbaby’; ‘doggo’ and ‘pet parents’, but I don’t think non-usage infers a lack of humour or fun and definately doesn’t indicate the depth of one’s affiliation with animals. I suspect that people consider the terms ‘cool’ (which - in my day - used to be known as ‘trendy’!)