The problem with young people today is that they don't realize how damaging their apathy and ____________ can be.

The correct answer is "Irresponsibility" because the sentence is discussing a negative trait that contributes to the problem of apathy among young people. The word "apathy" suggests a lack of concern or interest, and it is often paired with a lack of responsibility or accountability in one's actions.

Using "Irresponsibility" fits contextually to portray how a lack of responsible behavior can be damaging, enhancing the overall meaning of the sentence. The word is a noun that effectively describes a failure to take responsibility, thereby aligning with the negative implications of apathy.

Other options, such as "Responsibility," "Responsible," and "Responsive," would not appropriately convey the sense of detachment and lack of action that the sentence is highlighting. "Responsibility" and "Responsible" suggest the opposite of apathy and would imply that young people are aware and engaged, while "Responsive" refers to being able to react to something and does not convey the same negative connotation needed in this context.