This question is one big spoiler for Battlestar Galactica Season 2 episodes "Resurrection Ship Part I" and "Resurrection Ship Part II".
In Part I of "Resurrection Ship", Admiral Cain and Commander Adama both plan to assassinate each other after the successful completion of the mission to destroy the Cylon resurrection ship. Admiral Cain plans to order her XO to "relieve Commander Adama of duty", and it's implied that this should be done violently with the help of a bunch of marines from Pegasus. Commander Adama plans to order Starbuck to shoot Cain in the head, with Apollo there to watch her back.
When Starbuck tells Apollo about these orders, Apollo visits Commander Adama and expresses his discomfort. This prompts Commander Adama to consult the captive Boomer copy they keep in the brig, who tells him:
It's what you said at the ceremony before the attack, when Galactica was being decommissioned. You gave a speech, it sounded like it wasn't the one you prepared. You said that humanity was a flawed creation, and that people still kill one another for petty jealousy and greed. You said that humanity never asked itself why it deserved to survive. Maybe you don't.
The result of all of this is that Commander Adama decides not to execute the plan he ordered Starbuck and Apollo to carry out, even though he "has the drop" on Cain because he gets the chance to talk to Starbuck before Cain gets the chance to talk to Colonel Fisk. He says: "It's not enough to survive. One has to be worthy of survival."
Admiral Cain also calls off her plan to relieve the Commander of duty. Why?
Does she have a "change of heart"? Seems unlikely for someone with tunnel vision as severe as Cain's.
Does she realize that Commander Adama was calling off an assassination plot when he spoke with Starbuck while she was in Pegasus's CIC? It seems to me that she's too ruthless to let that soften her attitude toward Commander Adama. If she knew that Commander Adama had plotted to assassinate her at all, even if he decided not to do so at the last minute, it would be more reason for her to execute her own plan. She shot her previous XO in the head for simply disobeying an order, after all.