Cats use the litterbox and then lick their paws, as well as the rest of their body. If you pet your cat and then absent-mindedly eat something (like I've done all too often, unfortunately), you may become infected.
Throwaway for obvious reasons, but this would actually explain a lot. Oh god...
Anything that touches the cat's litter or butt might be infected. I.e. you'd have to keep the cat off your furniture, especially eating or food preparation areas -- every time. You'd have to not ever put your face on something that the cat might have snuggled against, or walked on. It's just not feasible.
Throwaway for obvious reasons, but this would actually explain a lot. Oh god...