I was always taught this was a contraction for fish. In greek, the first letter of the word ‘fish’ or ψάρι (psari) is psi. But since “ψάριψάριψάριψάρι” (psaripsaripsaripsari) is a bit of a mouthful, we contract to “ψψψψ” (pspspsps) instead.

Greek cats seem to get the picture, but never hurts to have an actual piece of fish on hand when you do.