If ancient people idealized fat women, why are ancient greek statues depict thin women?

What statues are you thinking about? Because even in those depicting “slender” nude women, many have what would be (in flesh) a belly pouch. A small one, but that would be it. And while their arms look toned, it is marble, and likely (in flesh) they would be a bit flabby and fluffy.

I’ll grant that they look in general fit, and not what you associate with fat. But they’re not what I would describe as the “thin” that is touted in even fitness magazines today.

Nope, more surface area on a fat woman. Not that there is anything wrong with that, it’s simple physics.

She was the “Before” statue. Her tribal elders were pushing the paleo diet.

IIRC, you will find quite a few stautes, from classic Greece to renaissance and later, where limbs, heads, or other “fragile” protrusions were added using another piece of marble. On a lot of older statues, those pieces have fallen off. The give-away is the smooth part where the two pieces of marble mate. Sometimes, too, a square peg-hole for the attachment; Venus de Milo appears to have one of these square peg holes on her left shoulder. Not sure what happened to her right arm, it may have simply broken off. That’s another problem with old statues - the fragile bits break off. (A lot of pharoah statues for example use the little beard as an additional brace going all the way to the throat.

More interestingly, the problem with “fat chick” statues disappearing appears to be the transition from mother-earth fertility religions to paternalistic, war-oriented male deities. This appears to have happened with the rise of male dominated city-states and armies. God became “Lord of Hosts”, i.e. man leading an aggressive army, and women and Mother Earth became marginalized. Why women’s sexuality would become suppressed during this time would be an interesting speculation for psychologists.

The Greek culture idealized the perfect athletic body type. With their empasis on sports, the “lard of hosts” look obviously did not match.