It is difficult because even the definition of critical thinking is debated. Though many try to teach critical thinking indirectly through other subjects, students may still go through their entire schooling years and be poor critical thinkers due to the emphasis of memorization.
Teachers who lack critical thinking skills are not qualified to teach them. Because there would not be any teachers trained in the discipline after the creation of the new curriculum, effective teachers will be few and far between.
In the process of teaching logic , such issues would be foundifficult by students and teachers and corrected over time. Which would act as a case study in critical thinking leading to additional real world example based learning.