You don't want the yeast to get access to any oxygen in secondary. Secondary should be a chance for the more yeast to settle out and to ferment that last .010 gravity point. Plus, you're keeping the beer off the old trub (dead yeast, protein, and hops) which can significantly affect the flavor of the beer if together for too long.
I can't remember the reason not to get more O2 in secondary, but it had something to do with changing the metabolism in the yeast. I think it makes the yeast try and reproduce instead of convert sugars to alcohol.