Title if you own pets?

Just a thought... so recently calling yourself "cat mom/dad", "dog mom/dad" has become trendy. I've owned two dogs whom have been put to sleep and now own a cat (brother could not bring it to Italy). However, I think it will be stupid if I call myself cat dad. I'm not a father to the cat. I didn't make the cat. I own the cat but she is not my daughter nor will she ever will be. My son or daughter will be when my kids when I marry a woman whom will share our offspring. Then, I will be glad to be called a dad. Has society gone too far ranking human babies the same as pets?
Title if you own pets?
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