I think this works because when we don't have to formalize (through speech or writing) our concept of the problem, our thinking is allowed to be less rigorous. We think we understand something, so we skip over it in our mind. Only when we formalize our thoughts do we realize our understanding isn't as complete as we thought.

Also, since we have to make sure our audience (duck) knows everything we know, we have to revisit concepts that perhaps we haven't thought about for a while.