I don't really agree with John Lennon. I think most of those wars were about power and land grabs, like Putin is trying to do today and the Kings and Queens were just using religion as a motivational tool to get peasants to fight for them. That and a compulsory draft.
Lots of countries are largely without religion now and they're still going to war and the leaders are still controlling the people and getting money for themselves. North Korea has everything Lennon thought would be wonderful and I don't think they're in Utopia.
Humanists believe we are all naturally good, but we don't know how much of that moral conscience was inborn or learned from growing up in a Christian world. The cave men did a lot of killing each other and raping women, it all came down to whoever happened to be strongest.
I look at the Old Testament as the beginnings of religion, the commandments were given and then the people sort stumbled along with it for a few thousand years.
For me, the "teaching us to be better" part doesn't really get going until the New Testament when Jesus was sent to refine the law from simple rules like, "don't murder," into. "don't even get angry, forgive instead." From "don't commit adultery" to "don't even lust after other women."