Cross-lateralization in the brain

The other day in my History & Systems class, I had a student ask me a stumper!
She asked if there was a purpose, or reason why the brain is organized the way it is, with respect to cross-lateralization.
Not being much of a neuroscience guy myself, I had honestly never given the question any thought, and have certainly never happened upon anything that raised either the question or had an answer.
More research required...