This bit of advice is actually---and probably intentionally---ambiguous. It can be interpreted to mean "care about your student' progress and welfare," but it can also mean "care about who your students are"---that is, impart knowledge only to those whom you trust.

To Klingons, knowledge and expertise are matters of pride. This includes both the understanding of history, rituals, and legends, and also the mastery of various practical techniques, such as those needed to be a successful warrior. Education and drilling continue throughout a Klingon's life. There are even some ritualized forms of practice, such as the {moQbara',} a type of martial art, and the {qa'vaQ,} a hoop-and-stick maneuver that hones the skills of the hunt.

Complementing the value placed on learning is an emphasis on teaching, the recognition that, in order to continue as a culture, it is important to pass on expertise to future generations. At the same time, to grow as a culture, it is acknowledged that teachers will learn from their students, another reason to be sure that the student-teacher relationship is one of mutual trust and respect.