There are multiple factors that determine what element, their aptitude with that element and ultimately what level of progress a person may develop as an element bender of the Four Nations.
Elemental bending is linked to:
- An as yet undisclosed genetic disposition linked to the various kingdoms. Each of the kingdoms has a predisposition for each element. Each claims to have been taught or influenced by a natural phenomenon or animal patron; fire by the dragons, Earth by the badgermoles, Air by the skybison and Water by the moon. No one may bend an element not native to a land of one of their parents.
- Cultural technique even within an element may take precedence and influence how an element is controlled. An Earthbender of Ba Sing Se and an sandbender of the Earth Kingdom deserts are both Earthbenders but each deals with their element based on the training of their respective cultures.
- Consistency and training; a bender may have the aptitude for bending but without training and discipline may never develop any significant ability. Consider Kitara before she left the Water Tribe. She was able to bend but it was uncontrolled and the results unpredictable.
- A personality profile does seem to affect how easily or difficult it is for a bender to master their element. If their personality runs contrary to their element's nature, they may have greater affinity or difficulty mastering it. Consider Aang and Earthbending, it was completely foreign to his personality.
- With discipline, subsets of that element can be controlled as well; fire can bend lightning, Earth could bend metal, Water could bend blood or perform healing. Air does not appear to have a subset skill.
- There is the lost art of energybending of which there are no living beings capable of performing it. The last known energybender was Aang who was taught by the lion-turtle.
- Aside from the Avatar, who is the living spirit of the world, no one has displayed a propensity or capability to bend more than one element at a time. Indeed this is the hallmark of the Avatar and the indicator of their reincarnation after death.
Each type of bending is also linked to a martial art technique. It is possible for a bender of one type of element to learn the martial style of another bending type, but they still will not be able to bend that element whose style they are imitating.
- Airbending is linked to Ba Gua Kung Fu; whose techniques are focused on circular motions and redirecting the energy of the opponent back upon themselves.
- Waterbending is linked to Tai Chi Chuan and is focused on feeling the flow of an enemy's fighting style and redirect that energy away from the martial artist.
- Earthbending is linked to Hung Gar (though there are others), Earth fighters focus on strength, power and resistance in their fighting technique. They are durable and strong fighters physically overpowering their enemies. They are also known for their ability to cause collateral damage to the environment.
- Firebenders are linked to Northern Style Kung Fu, which offers strong aggressive and defensive capabilities and is one of the most well balanced in terms of offense and defensive techniques.
The power to bend the five elements (air, earth, fire, water, and energy) is linked specifically to the nations (and people) of the Avatar World by an as yet unknown mechanism. With the exception of the Air Nomads, mixing of bending types does not necessarily ensure what bending abilities will manifest, or whether ANY bending ability will be inherited at all. Nor is it clear how the power moves between family members. Even twins of parents from two different lands can possess different bending abilities.
Since there are variant powers such as metal-bending (a variant of earth-bending, or explosion bending (variant of fire-bending), this might also denote why there is such a study of lineage among the people of their world, to attempt to predict what bending abilities and strengths might manifest in a family line.
From the Avatar Wikia article on Bending Arts:
Though each nation is affiliated to a specific bending art, not all
from any nation, with the exception of the Air Nomads, are born with
the ability to bend. It is unclear how the ability to bend is
distributed amongst the population or how closely it is linked to
heredity; even among identical twins it is possible for one to be a
bender and the other not. In the case of mixed marriages, the children
may be benders of either element if they are benders at all; for
example, firebender Mako and earthbender Bolin are brothers with
parents from the Fire Nation and the Earth Kingdom.
With the release of the Avatar the Last Airbender IP Bible, (kudos to Keen for finding it) several of the suppositions I made have been released and confirmed. I am copying them here in the event the source document link is later lost. Rationales are not always listed but some things are clearly defined:
From page one of the Rules:
- A bender's powers cannot extend beyond his native element.
- Only the Avatar can master all four elements
- Bending is the physicial manipulation of the elements and is defined by the skill, strength and stamina of the practitioner.
- The ability to bend is something you are born with. And not everyone in a nation is a bender. Only a small percentage of each population is a bender.
- Benders represent only small percentage of all people in the world. They may be born to parents of benders or they may be born to parents with no powers.
- A Bender's skill level determines the range of his attack
- A Bender's elemental powers never extend beyond their immediate area.
This document qualitatively proves no one but the Avatar can master the four elements and no one can ever bend more than a single element.