Was there some special reason the Black Knights simply couldn't tell the Fragments about who and what they were? The anime seemed to imply there was one but it never developed. The fact that the Black Knights aren't evil after all makes the entire story from that moment forward feel like a Could Have Avoided This Plot had they just up and explained themselves and the situation to the main characters as opposed to trying to kill them for no reason, prompting them to become more powerful and kill them in turn.
I guess the reasons could differ, as The Black knights in the anime are a lot different from who they are in the game. In the anime, it looks like that they were definitely evil and not having redeemable qualities like they had in the game. The reason why they said nothing to fragments was possibly because they were too arrogant to even explain why to them. It could have avoided a plot but actually, the anime was all messed up.
The game shows a bit more informations about it. The part of the reason is that even if they didn't have sait to Fragments who they were, Liselotte could already absorb them, even in her crystal. Indeed, Yukiko didn't die killed by Superbia like happened in the anime, but when she came to the Crystal palace to get revenge for Takahisa she had been absorbed by Liselotte. Yuka in the game and manga, also had been absorbed by Liselotte, so sooner or later, she would have got every of them as she awoke so Black knights had to kill them to prevent the destruction of the world. Another reason why they said nothing to them is more personal. In the prequel Before Story in the fandisk Resona forma, they had been humans before, and they all died in the mission (while they only turned into Black knights in anime), killed by Liselotte in a horribly way. And in the game, Larvaes magic which were inside them was eating their mind, making them slowly insane. They seem to have a personal hatred on Liselotte and the fragments because she killed them and like Ira said, they had no reason to tell about it to the fragments.
Anyway, even if they had said the truth to the Fragments earlier (Misao ended up by doing it in the game, and gave them three days to kill themselves or keep figthting) it wouldn't have changed anything. And the Fragments chose to fight and they managed to kill the rest of Black knights (as Avaritia and Superbia) as Liselotte.