Why is being the successor of rikudou so important that youd fight your own brother.
You don't just try to kill your bro cuz hes been entrusted with some feelings.
Being the successor clearly gives you a power up. Otherwise why get jealous?
Well think of it this way. Two young brothers inheriting some huge powers and both having different opinions on how to use that power, then suddenly the power shifts in a huge way.
One brother is like "Alright so daddy said I'm the guy so we do what I say and what I think is probably right, we should cooperate like this..."
The other is like "It doesn't matter, I was the guy all my life now I'm not the guy when it matters. You're not really the boss of me and I have some disagreements"
Meanwhile the path of the world is hinging on their disagreements
Especially after talking with the Sage, it sounded like he gave the Younger the title as some sort of social experiment for "cooperation." It just wasn't the right situation for them...at all. Personal concerns led to political concerns which led to a war.
I'm willing to bet this fight wasn't one sided and both had legitimate concerns/reasons and neither could resolve it.