The first two definitions are what I'm saying. So my point still stands. For instance, if you could have saved your child's life and didn't, you are to blame for their death. That's responsibility.
You could argue that a mother does not have any moral responsibility to her child or that a father does not have any moral responsibility to his child, but that's a different argument.
I did stay on topic. The topic was THE VERY THING YOU GAVE AN ENTIRE DICTIONARY DEFINITION FOR. And I gave an example of it. That's the exact definition of staying on topic: Topic: Responsibility Example: Men letting women and children have the lifeboats on the Titanic