The reason Rimuru became the Demon King "Tensei Shitara Slime datta ken", True Demon Lord Rimuru Tempest
The reason Rimuru became the Demon King was explained in Episode 8 of Tensura season 2. At that time Rimuru saw a lot of chaos happening in Jura Tempest and the many victims who fell as a result Falmuth kingdom attack.
In Season 2 Part 1 Anime Tensura, we saw the change of Demon Lord Rimuru Tempest after slaughtering 20 thousand troops of Falmuth kingdom allied with the Holy Church. Basically Rimuru doesn't know the Demon Lord's Change, but Eren says the Requirements as well as the possibilities Rimuru can do.
The Reason Rimuru Became Demon
Lord Rimuru saw many very sad events happening in Jura Tempest. All of this happened without him knowing who was outside Jura Tempest City at that time. When he arrived at the Jura Forest, Rimuru found a lot of "Sadness" one of which was the death of Shion and the destruction of the city of Jura Tempest.
After witnessing all these events, Rimuru was alone and pondered over all the things that had happened. After some time, Eren tells a tale that allows one to evolve into a Demon King and can resurrect the dead.
This fairy tale is a story passed down from generation to generation by the wizard dynasty of Sarion. The fairy tale tells about Milim Nava and her pet Dragon (Theory, Karna is similar to Milim's story).
In the fairy tale, it is told that a person has the possibility to become a demon king after slaughtering thousands of humans/victims. In addition, the resurrected Demon Lord has the possibility of resurrecting the dead.
Now Rimuru already has the Demon King's Seed and the condition for resurrecting it is by slaughtering more than 10 thousand souls (At that time Rimuru slaughtered 20 thousand souls). After listening to the explanations from Eren and the Grate Sage, Rimuru decided to become a demon lord by massacring the Falmuth kingdom's army.
The reason Rimuru became the Demon Lordwas To resurrect Shion and all the Tempest Citizens who had died. So, that's the only reason that is currently known. Because basically, RImuru doesn't know and has no interest in becoming the Demon King.