For what it's worth, Prometheus was a Titan, and Titan was immortal, so his liver regrowing the next day wasn't really that special. If eagle fed on his heart, or lungs, they would've regrown too.

The Greeks chose liver because it symbolized the defiance Prometheus had against gods.

There's really no knowing why the Greeks chose liver, or some specific Greek chose liver.

It could have been because the liver was regenerative and they were using the titan with the regenerating liver as another reference to humanity, or it could have been as someone pointed out because predators like to eat the liver first, or it could have been that you can take damage to the liver and live for hours afterwards in agony whereas the same amount of damage to the heart or lungs is apt to cause death to come much quicker.

Perhaps there are undiscovered variants out there were the eagle or a serpent or some other animal attacks his genitals, or his eyes.

But at any rate the Eagle ate his liver, it means nothing in particular, and at the same time it means every particular interpretation we can place on it.

I don't know about the Greeks but I know a lot of ancient cultures thought the liver was the most important organ (probably because it's full of blood).

For example in Persian poetry the word liver is found pretty much everywhere you would expect to see the word heart.

"You are my liver" is a nice/romantic thing to say to this day.

I thought they chose it because it tastes great with some fava beans and a nice Chianti.

Why would liver signal defiance?

I'm thinking the Greeks chose liver because it is the first thing that many predators will eat from a kill - large, more nutrient-dense than almost any other tissue, and relatively quick to access.