Practically critical thinking can be defined by means of skills or dispositions. While these skills and dispositions are known, there are still several difficulties in teaching and learning critical thinking.
Different people may define critical thinking in different ways, so different educators can teach different skills under the same banner. Also some people tend to equate critical thinking and any criticism. It may create a negative image of critical thinking.
Also there are issues related to the lack of knowledge about critical thinking: Some people don’t know how to learn critical thinking. Some people don’t know how to organize teaching of critical thinking.
A similar problem is a lack of recognition. For example, recruiters usually don’t ask about critical thinking, even if it could be useful.
Critical thinking can be hard to learn because people may need knowledge in other areas to understand new concepts from critical thinking. This may increase academic load.
We still don’t understand some aspects of critical thinking. For example, publications like this raise interesting questions: Critical thinking ability and belief in the paranormal, A Hergovich, M Arendasy - Personality and Individual Differences, 2005. If critical thinking isn’t correlated to belief in the paranormal, do we have good means to measure it? How can we measure and improve skill transfer from one area to another?
We may also have a problem with measuring critical thinking. There are a number of tests people can take, some of them are paid. But there aren’t many researches about these tests, correlation between them, and correlation with other metrics. Of course we can measure only academic performance, but we also need to know how critical thinking contributes to it.
There are also different social issues related to critical thinking. Some people are accustomed to being told what to do and when to do it. Having others make decisions relieves people of responsibility. Some people may think that their judgment is inferior to that of an authority figure.
So as you can see, different phenomena can prevent people of learning critical thinking. Fortunately, with time and effort most of these issues can be overcome.