Functional leadership theories are developed by studying successful leaders and identifying the actions and behaviors they show.
Extensive studies with a large amount of data make it possible to correlate what leaders do, i.e., their actions or functions, with their successful results.
[1] (Examples are given in brackets) Apparently some unknown people consider Adair's Three Circles Model too simplistic and outdated as it was developed in the 1970s and yet the Britishc Armed Forces (Army, Navy and Air Force), 50 years since its creation, still use it as the basis of all their leadership development programs.
Whether leaders are born or made is part of the question of whether human behavior is due to nature or nurture.
It is a short leap from functional leadership theory to the belief that if one person can do something, others can also learn to do it.