When writing an essay or preparing an oral presentation on one's professional competency and sense of personal responsibility, it is important, primarily, to project confidence without arrogance. The purpose of a presentation intended to demonstrate one's professionalism and leadership abilities is to impress the audience that the presenter possesses the education, knowledge (not always the same as "education"), experience, and maturity necessary to ascend the corporate or organizational ladder.
Obviously, in preparing a presentation on professional competence or in writing an essay on personal responsibility, the individual is attempting to market his or herself. To do that, the individual should describe his or her academic credentials, any additional, specialized education or training that has been completed and that would be relevant, professional accomplishments (for example, contracts successful negotiated, architectural designs that were translated into action, medical procedures successful accomplished, etc.), ability to communicate clearly to superiors and subordinates alike, lessons learned from past failures, and ability to assess and bring on-board personnel who can contribute in a positive manner. And, of course, the individual must be able to convey that he or she possesses the requisite leadership skills necessary to perform at the next level.
Demonstrating personal responsibility, as distinct from professional competency, entails the ability to project maturity and integrity. That means taking responsibility for failures as well as successes, and explaining what lessons were learned from both.
The ability to command respect -- a product of knowledge, experience, and personality -- is what the people at the top of the organizational pyramid are seeking. How one presents oneself, when given the opportunity, is vital in ascending the ladder.