He knew she wanted to help and that she had good intentions but the fear of what Valentino would do to her was stronger and he knew he had to get her to leave or else she would get hurt,so he had to get extra harsh with her and snap at her. 

Looking at Angel, he is selfless to the point of self-destruction.

He obviously cares about others and his loved ones but the one person he doesn't care about is himself and if you told this man that he deserved to breathe the same air as everyone else, he would gladly take numerous beatings just to ensure you don't and that shows how much he cares but also how unfortunately how little he values himself. 

It also shows,and this is a really hot take..but outside of Valentino and Vox and Vel..Angel's biggest Enemy and challenge is himself and its not the fact that others think he's a lost cause but it's the fact that it kinda feels like,subconsciously, Angel Dust wants to be one so people give up on him and that's not Okay.

He can't keep going back in the Ocean to drown himself after the people close to him keep not only tossing lifeboats/rafts but also keep physically diving in to save him and pull him out of the water and I do want someone to give him a reality check on that cause he's basically convinced himself that he can't be redeemed or saved or anything of the matter.

Honestly looking at this expression how Angel Dust was "mad" at Charlie does hurt cause you can tell he didn't exactly love snapping at her like that.