Hey everybody!
Izzy's player here.
So, the question is, why did Izzy flat out leave?
It's a rather complicated affair.
First of all, the obvious answer is that Garreth betrayed her, and therefore she couldn't stand being around him. This is true, but it doesn't explain everything. To add to this, Izzy entered a Virtue Extremity. Her Duty to protecting the world countered her loyalty to the Band exponentially. Therefore, thanks to both the stress of the situation, and the utter zealous belief that she had taken over her mind, she became very, very irrational. This in turn lead to a psychotic break thanks to the stress and the conflicting Virtues at play.
In the end of her farewell scene, I tried to write it as if her mental block was breaking, but by that point she'd made up her mind. There was no turning back by that point.
From a story perspective, her leaving did make sense. From a gameplay one it was... an odd experience.