The idea that those with the power in strength or numbers to kill others for their offenses are considered "right" because of it. My world at least likes to set up laws that those with leadership power are supposedly beholden to the same as any common person, and executions are left to the government only after someone's had a trial in which all evidence is presented to determine if they were or were not guilty of the crime they were accused for.

Execution's also reserved for higher crimes to begin with. Like... murdering your spouse because they weren't faithful to you, for example. An affair is a personal matter that people are expected to settle between themselves; killing someone the government hasn't determined as worthy of a death sentence is the actual crime.