I'm reading 'Drawing on the Right side of the Brain' and it's just discussing the fact that both sides of our brain think completely differently (of which I'm sure you are aware). The phrase 'on the other hand' relates directly to the other perspective considered by the left hand or 'right brain'; the reason why we second guess ourselves, or have a 'gut feeling'. I think this goes a long way toward understanding why we are full of contradictions before we come to conclusions. As Laz says 'we re-evaluate' on the information that comes to both minds.