My guess is that poor folks went out and found the beans lying on the ground. They were allowed to brew up the beans, because they were waste beans. They did so, and it tasted good.
The thought makes you want to gag a maggot, but it's entirely possible that the, ahem, "predigested" coffee beans are essentially "naturally roasted"...by the DIGESTIVE JUICES in the BOWELS of a RAT before passing out IT'S ANUS...(but let's not go there).
Ahem.
So, it might actually taste good.
And once somebody drank coffee with the poor folks, they discovered it taste good.
Puzzle on this one: who do you suppose was the first person to decide that cow's milk would be good to drink, and how did that come about? (The visual is, well, amusing and unpleasant at the same time.)
But why don't we dring dog's milk or cat's milk?
Self-preservation, IMO. Have you ever tried to milk a cat?