I am trying to distinguish accountability from responsibility, and your definition is no help. Accountability implies compulsion to answer to some external specified criteria, but responsibility carries an implication of authority, agency, and obligation to the mission itself. For instance, what should teachers do when the data-driven decisions of corporate vendors hurt the children in our care?
I looked it up because I am amazed at the human brain's capacity of justifying itself. We need each other, in order to see ourselves and our situations clearly. The brain is a master at self-deception. People have justified atrocious crimes by appealing to the concept of "it's for the greater good," or "the end justifies the means," or "it's my life, and I do whatever I want with it." Accountability is necessary.