So... You were the pragmatic part of Madeline, and guess what? A constant annoyance to her.
But after a few hours of climbing, Madeline thought "Maybe that Part of Me wants to be free?" That would surely solve her problems!
Of course, she wouldn't see you unless she was dreaming, so she set her bag next to Theo and fell asleep. In the dream, after some climbing, she reached a part where she was split in two. One half was her, the other was you. She said you two needed to talk.
Madeline: "I finally understand who you are. You're not my true reflection."
You were confused. You weren't?
Madeline: "You're everything I need to leave behind. You're cruel, paranoid, controlling..."
You were... Kinda hurt by that. Why would she say THAT?
Madeline: "No, it's ok! I understand now. I don't need you anymore."
You couldn't believe it. Was she just gonna... Abandon you?
Madeline: "I'm setting you free! We'll both be so much happier!"
You didn't want to be abandoned, becoming enraged at her suggestion and wrapping some tantacle around her for trying to leave you while you were trying your best to help Madeline out.
Frightened, Madeline starts panicking. Begging you to calm down while also trying to calm herself down with the feather technique taught by Theo, but you interrupt it and "cut" the feather in half.