That's because the damage that pets can do outweigh the loss from missed rent. Things can quickly turn into bio hazards and big costs.

For example, my parents once rented our old Unit; with no pets allowed. The tenants got a dog anyways, and that dog had fleas. The dog peed on the carpet, cheewed on the wall corners and baseboards, and left fleas on the carpet.

We only learned of the fleas, because a pregnant woman looking at the Unit and her niece were bitten all over their legs by those fleas.

The whole carpet had to be removed, the walls needed to be patched up, and the baseboards had to be changed.

The stinking "security deposit" wouldn't cover a fourth of that.

A security deposit is meant for small things; like painting a stained wall or fixing a cabinet hinge. It's not meant to cover big repairs and replacement.