Baptism reinstitutes that which was lost, so baptism is not so much a case of removing something that is there, as re-establishing something that was lost.
That clears things up a bit. But it also begs another question. If it is to restore God's will in favor of self will, then why even after baptism is the power of sin present? And if it does involve a reconstitution of will from ours to God's, why baptize anyone before they have a conscious decision to do so (i.e. infants), before they even have the self will to sin?