Of what authority are you speaking? What exactly was passed on?
The authority to spread the teachings of Christ in the same way that Christ spread them, and to interpret them so that they would be clear.
Scripture alone is about as clear as mud. The light of Tradition is the tool used by the Holy Spirit. Tradition includes such things as the Didache, which is a book of quotes compiled of the Twelve by their disciples. If one includes this in their Tradition, not only is Abortion implicitly wrong, but it is explicitly wrong, as well. The second section includes the command "Do not commit abortion or infanticide".
There are other teachings in the didache, but that is why Traditionally the Church has never accepted abortion.
The other authority was to remit (but not forgive) sin. Christ, speaking to the leaders of the Church, said "whatsoever ye bind on earth, it shall be bound in heaven. whatsoever ye remit, it shall be remitted in heaven." Remitting sin is not the same as forgiving. My Spiritual Father, Stavros Rousos, said, "a Priest never forgives sin. What he does is help the confessing person wipe the guilt of the sin away, because the sin itself has already been forgiven by God." He went on to explain that the Priest, instead of forgiving your sins, gives you the tools and advice and encouragement necessary to defeat the sin in your life to make sure you do not fall to that sin again.