[jeockammece]

I can't think of one reason a shelter would not adopt a cat out to almost anybody with a home or apt that allowed pets.

There are many reasons. Here are a few examples from recent applications:
They did not follow local ordinances.
There is no record of regular vet care for current or recent animals (often falls under not following local ordinances).
They have a history of obtaining and quickly returning/surrendering animals.
They are not financially prepared.
Multiple animals have been lost, stolen, hit by car or have run away.
People in the household are allergic and the animal will be returned if there's an allergic reaction.


And then there are debatables:
Cat will be declawed
Cat will be allowed outside

And sometimes odd return reasons:
They will return the cat for jumping on things or knocking things over.
They will return a cat for shedding.
They will return the cat if it is not a lap cat.