I always took the Last Gospel to mean that we cannot save ourselves. That we must have the gift of Faith which only comes from God....not from our will or another's will and not from our lineage.
Well, I think that the primary meaning is the same as the famous "born again" passages, where there are two types of birth, a natural birth and a supernatural, and this passage distinguishes between the two. But I do find the references to not by blood, not by the will to be very suggestive. These words were written by the Holy Ghost and likely have several layers of depth and meaning.