We need to find a word that must be support by the clause 'emotions are the death of leadership'. Basically, emotions may result in irrational decisions. We need a word such as intellect, thinking, or skills, which help a leader to make rational decisions.

The words - grievance, miscreant, and frailty - do not fit here with the context.
Sophistry is a trick word. It sounds like sophisticated or related to Greek philosophers, whom one may think wise and intellectual. Actually, sophistry means to trick someone by cleverly giving false reasoning.
We are left with one word - poise. That's it. Poise means maintaining a balanced mind.