It seems like one thing that a lot of people miss is that the council voting for peace was based on the deal Jayce made with Silco earlier in the episode. That deal required Silco to give up Jinx to Piltover, which he was never going to do.
When Silco had that monologue at the statue, he wasn't really contemplating giving Jinx over. He was finally realizing why Vander lost his drive to fight for the Underground's independence at any cost. This is why he says "Oh, it all makes sense now, brother. Is there anything so undoing as a daughter?". Just like with Vander and Vi in Act 1, Silco was now put in a position where he had to give up his daughter for peace between the Underground and Topside. Peace was never going to happen to begin with because Silco would never be able to live with himself betraying Jinx after having had to experience being betrayed by his "brother" (Vander).
I think Jinx blowing up the council room was more to show her solidifying the fact that Powder is now gone, and that her and Vi are not on the same side of this conflict now that Vi has made friends with an Enforcer (Caitlyn), who she used to despise. Which is why before Jinx left she says 'you've changed too, so here's to the new us.
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