The greatest lie, in my opinion, is that of the "blank slate". The idea that human beings are born without instincts, and that indeed, all modern ills are caused by society. This ties in with the whole "noble-savage" myth.
Human beings are not born as blank slates. You raise two people in completely identical conditions, they might grow up to be similar, but they will not be exactly the same. All human civilizations and races share the same basic facial expressions, emotions and capacity for language and abstract thought. We have instincts - for example, you could not raise a majority of males to be homosexual. The majority of males is, and always will be, straight. Only a few people are born homosexual, usually due to some error in the formation of the part of their brain which handles such issues as sexual attraction.
All human civilizations have crime, have violence and have language. The noble savage myth is exactly that, a myth created by some high-minded and nice liberal folk who wanted to get rid of racism - and that was a noble goal, no doubt about it. But we don't get rid of racism by pretending that non-white folks are "better" than white people. We get rid of racism by realizing that all human beings are exactly the same. The "!Kung San" (yes that is how their name is spelt) were originally held up has a poster child for the Noble Savage myth - until it was revealed that the researcher who claimed that they were "completely non-violent" was talking out of her rear end. The !Kung San weren't barbarians, but they did have wars, they killed each other, and did all those things all other peoples do.
Humanity is a great species. We do have the capacity for kindness, love, joy and wonder. But we are not perfect. The communists also made this mistake, thinking that through education, humanity was perfectable. The collapse of the USSR showed how that was a mistake.
However, there is hope for humanity. We realize that things like violence and greed are bad things. As our technology improves we might modify our own brains to more accurately reflect our ideals. It might take thousands of years, but I have confidence that we will eventually gain the ability to modify our brains so that we are not cruel, violent or primitive. I envision a day where rape, murder, gang violence and the like, are things of the past.
Humanity, as it is, will never get rid of crime. But who says we have to remain as we are?