I knew someone who worked in property management, and this is pretty much the reason. It’s not that pet owners are bad tenants, necessarily, but a bad tenant with a pet can just create so much more awfulness in such a short period of time, and can really irritate the bejeezus out of other tenants. (So can children, but you can’t lawfully tell people they can’t have kids in the apartment – or else some landlords likely would.)
Even ‘good’ (comparatively) pet owners often have to be constantly monitored that they don’t just let their pet shit on the sidewalk 12" from the door to the apartment building and leave it there forever. Actually picking up dog poop, each and every time? Put the tenant squarely in the “saint” category.
The not-so-good don’t bother taking their pets outside. They let them shit in the hallways, or – in one particularly memorable incident – let a large dog simply use one of the (carpeted) bedrooms as a bathroom, for the entire period of the lease, and left all of the waste there, permanently. When they moved out and lost their security deposit, they were shocked and angry, and threatened legal action – it’s not like they just let the dog shit just anywhere in the apartment, it was only that one room! What’s the big deal?! It’s “his bathroom”! (They had to basically gut the flooring in that unit, and paid out of pocket, since the tenants were too broke to make suing them viable.)
As a dog owner, I totally sympathize that this sucks, but if I owned properties, I can understand. After the 50th tenant complaint about dog poop left around on the property, bad smells from apartments, aggressive animals not handled property, and the like, I can see just saying “screw this”. A lot of humans seem to think that dog maintenance is basically “feed dog and give it water”, and don’t account for keeping the dog clean, vaccinated, exercised, trained and, most of all, properly handling the waste of the animal.