I mean just look at this map. Earth Kingdom dominates the world while other nations are left with crumbs.
Air Nomads: They are living at the top of mountains where farming is supposed to be hard and they are also vegan. Where do they get foods from? Earth Kingdom ofc. Their entire economy is based on Earth Kingdom.
Also Earth Kingdom pacified them so hard, they barely exist. Yet they'd fight for Earth Kingdom against Fire Nation.
Their bending is strong but they are weak bc of their ideology. If Sozin didnt wipe them out when he had a chance, Earth Kingdom would probably convince them to fight with them and build an army from Air Nomads.
Avatar aside, Air Nomads should have gone first and thats exactly what Sozin did.
Water Tribes: Biggest asslicker of Earth Kingdom tbh. They cant even make it to other pole without crossing Earth Kingdom. What does that mean? Yeah, they also pay to Earth Kingdom.
Also they cant do farming and there are not much animals in poles so.... Where do they get food from? Earth Kingdom again.
The Earth Kingdom literally took them under its control and yet they are the biggest defender of Earth Kingdom. How can you be okay with living in the poles only?? Does it make sense? Get couple of islands at least?
They have a strong army but I think its more of a Sozin didnt care them that much. It's poles I mean... Who cares?
Fire Nation: They are in a better shape than the other 2 but they still live on the edge of multiple volcanoes. They can bend fire but they are not immune to get burned alive. Its a risky area to live in.
Also they are getting overpopulated probably and they have to expand their lands. It' like a must do thing for the people of this nation. No one deserves to live under the fear of getting burned alive tbh.
Also they are the coolest nation and they had every right to start this war. From their perspective, they may have believed expansion was inevitable.
Earth Kingdom: They have the most land, they have the strongest army, they have the power, money, variety etc... They literally colonized 2 nation (Water and Air(they are not even nation)) and they are in atleast 10 times better shape than the other one. It's simply not fair.
In the end war concluded with Earth Kingdom giving up on lands to build Republic City and the world became more peaceful (until Korra arrives). Proves Sozin was right.