There are many reasons why it is worth teaching critical thinking. The most fundamental is that good thinking skills are essential for making appropriate decisions about what to believe and do, whether for personal decisions or civic ones, such as voting or serving in a jury.
Like many skills, critical thinking can be improved through education. Yet in a classical education designed to produce a well-rounded individual capable of acting reasonably in many different situations, surprisingly little time (if any) is devoted to teaching practical and general thinking skills.
It is worth teaching critical thinking because the personal benefits to the students, their employers, and society more generally are high.