Why is the President of the USA always deemed to be the leader of the free world when all he has been elected for is the leader of the USA?

Ask the foreign press who calls him this.

No American really thinks of the president in that way, it’s everyone else who does.

A 'leader' is the guy who's out in front, yelling 'This way!' over his shoulder.  Since about the time of Teddy Roosevelt we have been a world leader.  After WWII we were THE world leader.  For a while.

In those days (Post-WWII) the whole world was seen as a battleground between Capitalism and Communism.  The USA was seen as a leader (or THE leader) of the capitalist side, which we called The Free World.  So the president was the Leader of the Free World.

President Trump, though, was a man who would rather win than lead.  He wasn't really any kind of leader, either of our country or our allies.  'Leading' in the international sense means pulling countries together, forging agreements and treaties.  That was just not the kind of work Trump did.   'Leader of the Free World' was just an impressive-sounding title to him.

Because for many decades, America's military and economic might meant they could boss those other free world nations around.

Still can to a point.

For instance, what would happen to Western Europe if the USA threatened to pull out of NATO?  Their militaries are in bad shape.  Germany is having trouble getting more than just a few of its fighter planes in the air right now.