It's a funny old thing, backwards compatibility. Up until the PS2 first entered our lives at the start of this decade, it was almost a non-factor in gaming. At that point, the only console that was fully backwards compatible was the Game Boy Colour. Okay, there were add-ons for the Sega Megadrive and Game Gear that let you play Master System games, or even further back, a Colecovision peripheral that added full compatibility for Atari 2600 games, but ultimately you had to pay extra for these.
When the PS2 hit, it was the first time in western history that you could play most of your games from the previous generation of the console on your brand-spanking new machine. Only a small number of games were listed as incompatible, and even this didn't prove strictly true in all cases. My old PS2 flawlessly played International Track and Field despite claims that this would not be possible.
Of course, when you look back, the PS2 was the only home console of the previous generation to feature backwards compatibility at all. The Gamecube saw Nintendo finally abandon the cartridge format, Microsoft's Xbox had no predecessor to inherit a library from, and of course, poor old Sega had hung up their console-making tools for good following the underrated and under-performing Dreamcast.
Again, Nintendo stuck with full backwards compatibility on the original Game Boy Advance and remade SP version, rendering it capable of playing all GB and GBC games. However, support for these titles was dropped by the time of the third remake of the console, the Game Boy Micro. When the DS arrived, it too would only allow GBA games alongside its own titles.
So it seems a little surprising that when the current console generation came about, the idea of backwards compatibility being reduced and (in some cases) dropped was treated as such a stab in the back to console buyers that you'd think it had always been a standard feature, rather than something that was still relatively new.