The most fundamental reason for teaching critical thinking is that good thinking skills are essential for making appropriate decisions about what to believe and do, whether for personal decisions, vocational decisions, or civic decisions, such as voting or serving in a jury.
Like other dispositions and abilities, critical thinking can be improved through education of all types at all levels. It is teachable if we work at it.
It is worth teaching critical thinking because the personal benefits to the students, their employers, and society more generally are high. Personal decisions, decisions within our vocational pursuits (at whatever level) and decisions we make as citizens of a democracy require critical thinking in order to be the best possible. We need the best possible in order to survive in this difficult world. Without a well-informed, critically thinking citizenry, freedom and democracy cannot endure.
But even for residents of non-democratic countries (which includes those without a meaningful vote), critical thinking is needed for wise personal decisions, useful vocational decisions, and decisions about how to be part of the society.