Why must any nation, whether of the "free world" or not, try to take on the task of "leading" others?

A very simple question, one that shouldn't require the use of baby-talk to explain it, but apparently there is at least one person here who just doesn't seem to be capable of understanding something so simple, so I thought I'd get some feedback from the more intelligent ones here.

The United States is often referred to as the nation that "leads the free world". Why? If that's the case, then the citizens of those nations that it pretends to "lead" should be able to vote in US elections.

Why must any nation, whether of the "free world" or not, try to take on the task of "leading" others?
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