Ok maybe I'm misremembering this but wasn't Cyric in Love with Midnight "Mystra". And she went for Kel? I quit following it a lot after that, but it seems to me unless Cyric went for the if I can't have her no one will, I'm not sure how likely it seems to me that he would kill Midnight.. or am I wrong on that?
Well, Cyric got spurned by Midnight, and being of the Chaotic Evil sort, compared to her Neutral Good, he got -very- jealous and killed Kelemvor himself.
So Midnight declared HIM -her- enemy, and sought to get back at her.
And then they became gods, carrying on them grudges.
From there, Midnight, now Mystra, actually denied Cyric's clerics access to their magic (which is well within her ability, as divine magic is still part of the Weave) because they were evil. This touched off a bit of a divine debacle.
Meanwhile, Cyric wanted to get back at Mystra for that, in his insane way (now that he's god of madness as well) and so he decided to put a bounty on Kelemvor in the Grey Waste (not realizing Kel's soul was in his own sword, the Godsbane, aka Mask).
This caused the dead souls of the Grey Waste, tired of their treatment, to rally behind this Kelemvor name, and start their own revolution in the afterlife.
Lord Ao figured all this was unacceptable, so made Kelemvor the god of the dead, taking that away from Cyric. (Which he took out on Mystra).
Cyric's beef against Mystra wasn't one sided, and while insane, was certainly understandable from his point of view as god of death, strife, murder, madness, and lies (many parts of his portfolio which were later taken away)