Well, part of her other issue would be recognizing that her duty is not to kill him, and that it was never to kill him. Her killing of him is downright unjust. The only reason she wants him dead is due to a personal vendetta that isn't even justified when analyzing the context of the universe.
She was a sworn Kingsguard to Renly Baratheon. She watched him get murdered by a shadow right before her very eyes. She was then blamed for said murder and the guards tried to have her killed. What would have happened if she died? It would have mattered naught to Stannis. He was butchering his brother and to hell with the fallout. That isn't just.
Stannis is entirely responsible for this chain of events.
Of course she is justified in her quest for revenge. If we're considering revenge a just cause at all. I think you're taking things to a meta level that doesn't begin to appreciate or recognise personal connections and conflict.
Sure, it hardly matters in the "context of the universe" but then almost the entirety of the plot and character interactions don't matter in that sense either. It matters to Brienne and that's what's relevant in this whole mess.