[Nightengale]

It's not really that confusing. It was not answered in clear detail, but the hints were clearly all there.

Sion's psyche and mind were clearly being slowly eroded away by the 'Mad Hero' residing inside him for the last few episodes, and because the Mad Hero intends to sacrifice Ryner who has the Solver of All Formulas inside him, Sion decides that before he completely loses it, killing Ryner is the best course of option as a mercy kill. ( Apparently being sacrificed is a fate worse than death. )

Sion has the Mad Hero inside of him. It was 'gifted' to him by Lucille back at ep3, when Ryner refused to escape prison and Sion made his first visit to the Eris Household. You know, the trial thing that Lucille mentioned but was not shown to us viewers.

Lucille has the Weaver of All Equations ( or is the Weaver himself ) inside of him. How he got it, we don't know, but it's also highly implied that was the reason he managed to beat his father.

As for why Ryner has the Solver inside of him, we don't know. That part definitely wasn't mentioned in the anime at least. But it's something that is known to Ryner's Dad and Lucille. Ryner's Dad presumably put the soul of his mother inside Ryner as some form of safeguard against Alpha and against the Mad Hero/Lucille so that... she could pop out to reason with Lucille? Either way, Mommy Ryner was clearly something that was implanted inside Ryner as a safeguard.

Sion's really all there is to him. He is torn by his true self and the Mad Hero inside of him. But I think another reason for the conflict within Sion is that Sion is someone who pursues what is right or better for the greater good and what the Mad Hero offers is something that leads to that goal. So he does not entirely denounce the Mad Hero ( he allows Mad Hero to take over his mind after all ) but emotionally, he does not condone it because it betrays Sion's humanity in the form of the friendship and kindness in him.