Both!

The flavour is similar to that of the question, "Is it heredity or environment?"

Based on my observations, obviously not scientific, it seems the right ratio is about 50-50. 50% of the qualities of a leader are there at birth; 50% of the qualities of a leader are created through life experiences. If a person has natural-born leadership qualities but is never given the opportunity to use leadership talents then we will never know that person as a leader. If a person possesses natural-born leadership qualities and those leadership qualities are recognized as talents, enhanced with knowledge, and honed with skills then that person, given opportunity or taking opportunity, becomes a leader.

Some folks are born with the right stuff for leadership, which [if boiled down enough] can be summed up in 3 words: intelligence, drive & self-control.

Some of those folks are able to put those qualities to use.

Some folks are not able to put those qualities to use.

Other folks who possess bare-minimum natural-born leadership qualities can learn to be successful leaders if they have ambition and good ‘guides’ & opportunities to learn from leaders [especially, in early life]. 

Maintaining leadership capability requires constant self-and-character development, otherwise it is lost.

Sometimes, dormant leadership capabilities are ignited into full force by exceptional circumstances and crises. This is rare, but it happens.

Born Leader?