1. ...are proud of non-God belief. NGB is an important part of their identity.
2. ...consider God-belief a significant cause of violence (and other ills). Think a world without God-belief would be more peaceful. Think this is obvious.
3. ...consider atheism categorically incapable of causing violence because no one ever says "I kill you in the name of the no-God." By implication, metacognitive reports in regards to one's own motivations are seen as both important and reliable. If you say "I did the bad thing because FDR told me to," that's the reason. To phrase it less generously, self-ascribed motivations are taken at face value and assumed to be causal. ("I killed her because I loved her"-- "cause of death: love")
4. ...think or assume western state violence (WSV) is either generally well-intended and therefore not actually violence so much as, say democracy and freedom (good violence = 0 violence) or, far less often, that it is actual violence but simply not religious because it's rarely (NAs seem to assume never) accompanied by God-words. So WSV is either non-religious nonviolence or non-religious violence. Either way, WSV is entirely distinct from religious violence.
5. While atheism is responsible for 0 violence, religions, whose adherents sometimes proclaim their God belief as the reason for their violence (and when they don't, c'mon you know they're thinking about it), are not all equal. Rather, violence varies by religion, depending on
Bonus Q & A
Q: What if an atheist kills someone?
A: They do it for non-religious reasons.
Q: Doesn't that make non-religious reasons a cause of violence?
A: Yes, but...
Q: So atheists can be violent, but atheism never is?
A: That's right. Atheism is the good and the true and people who follow its teachings can call themselves Brights, or, to paraphrase, The Finders of the Way.
Q: I want to be good and true. Can I be a New Atheist?