The rage comes from guilt.
Even if the woman felt she had no choice, deep in her heart she knows she killed her baby. And when you point this out, it hurts her. Since alas few pro life types usually state their condemnation of these murders with the mention that God can forgive them of this sin, they have two other choices to deal with the guilt... one, drugs or suicide. Two get friends to tell them they did not do anything wrong, and so they project this guilt as rage on others.
You're spot on LadyDoc.
I spoke to a retired pastor a few years ago, who also has a PhD in Counseling Psychology. He also was an adjunct college professor in his "retirement." He has counseled thousands of people over his career. He said there were three conditions that inflicted the human soul and were so devastating that only the intervention of God seemed to bring complete success and peace:
1. Addiction
2. Homosexuality
3. The guilt of Abortion