In Harvard Law School, Barack Obama was President of the Harvard Law Review and was sort of the "old man" among his fellow students there.
Most of his fellow students in the Harvard Law Review were a few years younger than he was. Often he felt that disputes between opposing parties were childish. He had considerable skill in getting opposing parties together by splitting the differences between them; that is, by working out compromises. He was a very effective mediator at the Harvard Law Review.
As a U. S. president, Obama would not be the "old man" mediator as he was on the Harvard Law Review. In my recollection, a potential president tries to demonstrate a record of leadership, not of mediatorship. A commander, such as a commander-in-chief, is expected to be a leader. A commander-in-chief is not a mediator-in-chief.
Is there really a difference between a mediator and a leader?
In contrast, a leader seeks to advance particular positions. Compromise may be necessary, but compromise is not the main goal of a leader, as it is of a mediator. A leader seeks to persuade an opposing party as to the merits of his/her positions. Sometimes the positions of the opposing party do not merit compromise, at least not significant compromise. The leader seeks an optimum solution, one that is as close to the leader's position as possible.
The mediator seeks a middle ground so that both sides will accept a compromise.
A leader is an advocate. A mediator is a neutral party. A leader seeks to pull movement in a clear direction, in his/her direction. A mediator seeks to push opposing leaders in opposite directions towards each other.
A leader on the political right seeks to pull the political left towards the political right. A leader on the political left seeks to pull the political right towards the political left. In contrast, a mediator seeks to push the political right towards the political left and push the political left towards the political right -- always seeking the middle ground, whatever the opposing values and issues are.
A leader wants to accentuate a difference and pull the opposition in his/her direction. A mediator seeks to split a difference and encourage opposing leaders to move in about-face and opposite directions.
Many years later, leaders sought to abolish slavery completely and by the Thirteenth Amendment to the Constitution, slavery was abolished.
A mediator would have sought a compromise. Perhaps abolish slavery in some states and retain slavery in other states; perhaps abolish slavery for men, but retain slavery for women; perhaps abolish slavery for adults, but retain slavery for children.