Being neutral may not always be the best option, by not allying yourself with one of the sides you're not protected by another force. You're effectively on your own. But you're also potentially an enemy to every single side, meaning your elimination would be positive.
Koty's reasons for war - Eli kidnapped his kids, led to them being brainwashed by the SF, Eli is his antithesis and a total dick, settling old scores.
Fatet's reasons for war - He wants to unite the three opposing factions against the potential threat of Plex.
Eli's reasons for war - Self defense, keeping the peace.