This is anecdotal, but I've loved animals my entire life. I was going to be a vet, but changed careers because my internship made me afraid it would ruin my love of animals.
I've had a very rough twenty years. I was married to a man who turned out was abusive to animals, so I gave up my dream of having pets. When I bucked my entire culture to divorce him, I fought my way back to enough financial security to own them again.
My first pet was 5 when I got him. I had three years of his endless health problems, but I loved him and he died. Then I got a couple of puppies and I love them, but...I don't think I'll own any more dogs. Dealing with other pet owners has been a nightmare. Off leash, poorly trained, outright dangerous dogs everywhere.
But even more to the point, I'm a terrible owner for them. I'm allergic, so I only play with them before my shower. And my mental health has me barely able to function some days. And I'll never be able to own the property they need to truly flourish. They deserve better than me. So I agree. Poor mental health can be exacerbated by pet ownership.