That angry atheist you speak of isn’t adherent to any dogma, typically, they are pissed.
The angry atheist stage is a stage of loss. You know how when someone dies, you go through 5 stages of recovery; denial, anger, bargaining, depression and acceptance?
When you give up god, you go through some of those. Anger for sure, but I kind of think that’s the first and last stage. Why anger? At first, it’s because it’s like your best friend died.
Jesus was probably your best friend and closest confidant. When you discover (and yes, it’s a discovery, not a rejection) that he never existed, it’s a very sad thing. You mourn the loss of that close friend, just like an actual death. You go through the other stages of grief and come out angry again.
Why again? Because you have come to realize that the myth of religion was perpetrated upon you. You have been victimized and for what? Because the people who taught you these myths were either too afraid to analyse their beliefs or maybe never knew that they could.
You realize all the real harm that has come to yourself and the rest of the world – for a literal myth that put the fear of hell into you.
After a while, all that goes away and you come to terms with life again and realized nothing changed. You can still love, laugh, cherish, cry, mourn, rejoice and be totally fulfilled. It just takes a while.
So if you ever wonder why you react so strongly to an atheist’s arguments, maybe you’re in step one. Denial.