A more thorough explanation:

A vexed question is a question that is often argued about but never seems to be settled. It can also refer to a question or point that has been decided differently by different tribunals, leaving it in doubt.

For example, the question of whether or not the death penalty should be legal is a vexed question. People have been arguing about it for years, but there is still no clear answer. Another example is the question of whether or not climate change is caused by human activity. Scientists have different opinions, and the question remains unsettled.

The term "vexed question" comes from the Latin phrase "vexata quaestio," which means a question that has been disputed or debated.