The title pretty much sums it all up. When selecting quarter sawn lumber, why should the very center (pith) be avoided?
The pith is what remains from the time when the tree was but a lad. It's soft and weak. Using it in woodworking would be like making something out of a bush. When the pith is exposed on two faces of a board, it will often crack and fall out.
It's also under stress. If you look at 4x4 posts at HD or Lowes, you'll notice that many of them have a split that runs from one face down to the pith. If you're going to make something that includes the pith (called "boxed heart"), you can make a cut that mimics this split and reduces the tension. Japanese woodworkers like to make this cut and then insert a piece of softwood to cover it up.