Until the age of puberty, I'd argue children don't necessarily know any better. They are still learning and are going to make mistakes. These are not sins! Sins can only be committed by an individual who knows better and even then, there are minor sins we all commit (as we are imperfect) and major sins which can have serious consequences for both parties involved.
I think children are born pure and innocent, for the first 11 or so years of their lives, their parents/guardians are the ones who have that responsibility to ensure their child knows the difference between right and wrong, but also how to deal and treat others. That being said, there are extreme cases where kids experience trauma and end up committing horrific crimes/sins...(The James Buldger murder comes to mind)
My issue with religion sometimes is that its followers can be absolute about things which there does need to be a balanced approach to. Sin would be a topic which you need to consider personal circumstance...i mean a hungry child stealing bread isn't a sin is it? Someone stabbing their abuser during an assault isn't murder is it?
Kids need guidance and even well into puberty they will continue to make mistakes but at least around puberty they are able to differentiate between right and wrong...
We all sin, it's natural. I think the point of sin is to learn from your mistakes and grow as a person who knows that certain paths lead to spiritual and mental destruction...it's a lifelong process and tis the nature of this life.