I am an atheist so I happen to know a fair bit about the “all wars are caused by religion” statement. The statement needs to be changed, it is not correct.
You could say “religion has had a role in every war” and it would be correct. However, you could also say “technology has had a role in every war” and it would also be correct.
When you look at the war in Iraq and Afganistan, you can certainly see Muslims flying in to buildings, and you can also see Bush saying “god bless america” and all that good stuff, but Bush did not declare “war on terror” because Christianity is “better and true”, and he did not declare war to get any virgins or to convert the Muslims. Bush declared war for revenge, opportunism, and to settle an old disagreement and to finish what his father started.
Bush did use his religion a lot to get people behind him, and maybe used his religion to manipulate the public at times, but he did not declare war because he was Christian.
This is why I say “religion has had a role in every war”, but that is expressing a totally different thing to what people feel and think when they claim “religion causes all wars” or something like that.
I think, when people claim religion causes war or all war, they are remembering the days when religion did in fact be the cause of most war. I also think they are probably trying to express their observation that religion gets used to manipulate people in to war. However, overall it is a kind of generalizing poorly worded statement.
I would scrap “all wars are rooted in / cause by religion” and instead go with “religion is the warmongers most useful and most used tool”.
We could sit here all day and look at different wars, we could bring up how Hitler used to have “god with us” on his soldiers belts, we could look at the conflicts in the middle east and spend all day talking about how religion is always around when war shows up, but it is also here in times of peace.
Religion is always there, and it some times has a role, in fact it quite often more than not has a role, but you can’t really throw about words like “caused, rooted, motivated” and so on. The actual cause of war is usually something else, even if religion some times plays a role.