Short answer is: Westwood Studios was bought by EA.
Of course, it's more complicated than that, but not by much. As you know, C&C was split between what became the "red alert" universe with the typical USA/Russia/etc factions and the "Tiberium" universe with CDI/Brotherhood of Nod. Both had their ups and downs. And both were competing with, say, Blizzard and their Warcraft series followed by Starcraft. But I don't think it's competition with Blizzard that killed them at all. Most RTS gamers are going to play both unless they just don't like the style of one or the other. I've certainly played both. But Blizzard being more successful as time went on did, I think, highlight how Westwood's quality was becoming... inconsistent. Red Alert 2 and Yuri's Revenge were loved and seen as well made games. C&C Generals and Zero Hour were seen as innovative... but very messy. And for good reason; gods, they looked like shit if nothing else. Previous titles made with obsolete graphics had more appealing visuals a lot of times. So, when Westwood put something out that wasn't up to the standard people expected of them, it should be no surprise that they'd turn to Blizzard or other companies.
There's a documentary on YouTube I'll post if I can remember the name of it. The author breaks down things in great detail far better than I could from scratch.