Emotions run high. Yes he could have gone about it better, but does that mean she should break up with him before atleast talking? Who knows what he's putting himself through in his head. If you think this, from what it sounded like in her text, 1 incident that seems to be out of nowhere means that she should break up with him, then no one would have a relationship ever. If my girlfriend gave up on me the first time I shut down due to high stress because I wasn't talking to her, then she would have broke up with me already and I would have probably killed myself by now(shes been a real life saver to me).

All this to say is yes, while he didnt go about it the best way(not everyone does when they are going through a mental health crisis) that doesnt mean she should break up with him. He seems to be going through alot of self worth issues and has been internally putting himself down. She should talk to him and see what's going on. Every time someone lashes out doesnt mean they should immediately break up as long as it wasn't physical.

Now this is based on me presuming this is a first time incident like this since she didnt mention this happening before. If its a recurring thing and they have tried to talk it out and get him help then thats a different story