Submerging your face/head in cool water is an effective way to manage an emotional overcharge. It tells the brain to slow down your heartrate and breathing, so you won't drown.
Koharu really was stronger even if her past, she got crushed but never took the easy way out, her familiar love really is the strongest, noticing how her mom was looking allowed her to try one more time, maybe it wasn't the only time she did, it's sad but that was her reality ... and now she sees Hozue thinking about it instantly.
I can understand koharu's anger, she had it rough but never gave up in the end. And now one of the worst people in her life is wanting to throw it all away over a class argument. No, you do not get to take the easy way out. Koharu will make sure of that.
Koharu: You welcome death? Your punishment must be more severe.
Hozue: Torture?
Koharu: No; Succor.
Hozue: Wha?
Koharu: [Administering Tactical Friendship Hug with Underbarrel Comforting Back-pat accessory] That's right. Cry. Let it alllll out.