PS1 emulation was perfect for the PS2. When they made the PS3, that emulation was carried over. So the PS3 can play all PS1 games.
The PS3 originally had a piece of PS2 hardware installed that allowed it to play PS2 games. However adding this hardware increased the cost of PS3 production and as such, also increased the price it costs to buy.
Sony removed the hardware, but decide to use the same type of emulation for PS2 games, that they were already using for PS1 games. The problem was, that this emulation wasn't perfect, so rather than working on it and fixing it, they decided to remove it completely and gave the excuse "we are working on making new features and additions to the console rather than spending time and resources working on something old", they also pointed out that PS3 users didn't want PS2 emulation, but new PS3 features.