You wouldn’t think there’s that much meat on a cat, particularly where people are hungry enough to devour cats.
Perhaps in China it is hunger motivating this, but I'm not convinced, given my experience last year of visiting a very small village in Viet Nam, not too far from the Chinese border.
I may have the order backwards, but the gist was that one eats cat one time in the first half of the lunar month for luck, and eats dog once in the 2nd half of the lunar month for luck. These villagers were not starving, their water buffalo were healthy looking, as were the crops in their fields.