This does not mean that the PS4 controller won’t work with the PS5 console as a whole. You can still use the PS4 with the PS5, but you can only use it to play PS4 games, but games designed specifically for the PS5 will not be playable with the PS4, so you will need to buy a new controller if you’re playing with more than one player.
As to why the PS4 controller will not be compatible with the PS5, according to Sony, “We believe that PS5 games should take advantage of the new capabilities and features we’re bringing to the platform, including the features of DualSense wireless controller.” It is a bit of a pity as we’re sure that PS4 gamers will probably have a couple of controllers lying around that they were probably hoping to reuse, but unfortunately unless Sony changes their minds, you’ll need to shell out a bit more money if you want to play local multiplayer with a friend.