Perhaps a tiny bit . . . impulsive?  
I'll have to go back and replay that scene, but as I recall, she didn't really even want to hurt him then. She felt desperate and didn't know what to do. Looking back after learning more about her story, it's more like she felt her entire world was threatened. She considered Alex to be her anchor and felt that MC was threatening that relationship. It was certainly a crazy thing to do, but it doesn't necessarily make her crazy.
We can also agree to disagree too if need be. 
In short, I am on Team Izzy and I encourage you to give her another chance.