How does element dominance work in Avatar? Even though I learnt this concept from the Naruto series, it really makes sense:


When you blow (wind), fire will increase... so fire > wind
When you throw water on fire, it diminishes... so water > fire
When you smash water against it, it will have no effect on solid (earth)... so earth > water
And so on...


Following this logic, why can't waterbenders beat firebenders in Avatar (The Last Airbender)?

I also noticed that Aang himself, who is an airbender, could defend against firebending with his airbending skills. (note that I am referring to those earlier episodes when he was just an airbender (season: 1, episode: 1-5))

How does it work in Avatar? Which elements dominate over each other?

Additional Info:
few assumptions work in (Naruto) ninja world, that I didn't consider to include in the question because the question is actually focused on AVATAR not NARUTO


Element user's chakra flow matters in chakra domination. Example: Naruto vs  Third Raikage
Combination of chakra elements. example: Water+Wind > Fire
It works a bit differently in Avatar.

Firebenders draw they power from great sources of fire. The sun is usually the strongest one around (with the exception of Sozin's comet, when it arrives every 100 years). Water benders draw their power from the moon.

Therefore, at night, the water bender will usually win, while at day the fire bender will usually win. Since the fire benders were on the offense, they get to decide when to attack (during daylight).

Also, there seem to have been a lot more fire benders than there were water benders (also, the water benders were separated into two very faraway clans). 

Last but not least, in Avatar, the relationship between the elements doesn't seem to be that of dominance over one another, but rather, Earth and Air are opposites, while Fire and Water are opposites. It's not that one is stronger than the other, but rather two sides of the same coin.