Why can't you play ps2 games on a 120gb ps3?

Answer 1

To make the PS3 profitable and have it quit selling for a loss Sony stopped making PS3s that could play PS2 games long before the release of the PS3 slim. The only reason you could ever play PS2 games on the first PS3s was the game catalog for the PS3 was next to nothing. Once the catalog of games increased they dropped the ability to play PS2 games.

Answer 2

No the only PS3 consoles that play PS2 games are the early PS3 models with 4 USB ports as can be seen on the related link to the PlayStation Knowledge Center.