Yes, it is a mental disorder. These people take in more animals than they can possibly care for or afford. It can range from not turning away any stray that they encounter, or actively adopting animals from shelters. It’s not that they don’t mean well, initially.
I used to deliver Wheels on Meals in Chesapeake, Va. There was one house where the owners (old man/woman) had a huge hoard of cats. We’d knock on the door, then step back and hand over the meals at arms’ length from outside when one or the other came to the door, the stench was so bad.
The city subsequently moved in, removed the owners to a nursing home, removed cats, dead/alive, and then burned the house down, after condemning it, it was so bad.
In most cases, they don’t have much money, nor are they very well organized, and they start out with just a small number of cats and don’t get them fixed. It takes a VERY short time for a small number of cats who are reasonably well-fed, sheltered from predators, and not fixed, to turn into an amazingly large number of cats. Start with just one male and one female at least 6 months old (the age at which they can begin to produce kittens) or even just one female who was pregnant when she first turned up, and one year later the original female has produced two litters and all the females in her first litter have already produced their first litters.
By the time the first litter is getting to fixing age, the food bill is already challenging the person and the bill to fix half a dozen female cats is just too big to handle. By the time the second round of litters arrives, the problem is big enough that the person knows full well that calling the SPCA or animal control for help will result not in the fixing of all the cats, but in the euthanasia of all but a couple. Given that these are usually lonely old women, fearful of being abandoned themselves when sick or hungry, they just can’t bring themselves to do that to their affectionate little housemates.
The states and counties end up spending so much on euthanasia and rounding up ferals when there’s a rabies outbreak, and on dealing with with out-of-control hoarding situations discovered way too late, that I think it might be better and cheaper for everybody if state and locals governments footed the bill for free, no-questions-asked, spaying and neuterings of all cats and dogs that anyone brings to a vet or shelter and asks to have fixed. Always a lot of potential for abuse with blanket government funding of anything, but this problem just doesn’t seem to be getting any better, and the government/taxpayers end up paying anyway, after lots of animals and some people have suffered a lot.