Here's my thought train during that moment:
Okay, Edelgard just betrayed me big time. So many emotions, none good. Then she reveals she's the main antagonist up to that point... livid.
Win the battle and Rhea DEMANDS I kill her. My initial reaction is to off her... but then, wait. Why is Rhea so aggressive about this? Didn't I just learn the lesson in Caspar's support about jumping the gun rather than waiting and getting more information? No, if anything we should throw her in a jail cell and get names/schemes from her so we can stop all she is up to so I chose to spare Edelgard.
Then Rhea goes nuts, gives me the if you aren't with me your against me speech and reveals her true form... like, what? I just didn't want to kill the traitor before interrogation and you're going to flip out on me without asking for my why? Yikes, I am glad I chose to spare her now cause that is not how I operate (do what I say when I say it type leadership has never worked for me).