One might argue that the skill of critical thinking is the sum of the goal of higher education. I certainly take that view. On the other hand- we don't really have a good definition of exactly what comprises critical thinking. Without a concise definition, it is difficult to answer the question (see the last paragraph below).
From a purely anecdotal perspective of a teacher though: when you see students come into an engineering program as freshmen and leave as seniors, you have absolutely no doubt whatsoever that critical thinking, in every sense, can most definitely be taught.
Here is an excerpt from a paper that I have published on the topic (if I don't remember to put the link in, please leave a comment to remind me).
Excerpt from How engineers learn: a study of problem-based learning in the engineering classroom and implications for course design (Mayer and Stone, 2013)
It can be said that the most important quality in an engineer is the
ability to think critically—to analyze a given proposition from a
variety of angles and determine its strengths and weaknesses.
Critical thinking is generally accepted as a primary goal of higher
education (Mason 2007, Abrami et al. 2008, Bailin and Siegel 2003,
Sheffler 1973). As educators, it is our responsibility to build these
skills in our engineering students, or we will produce engineers who
can pass courses but who cannot function in the workplace. Therefore,
both the teaching and evaluation of critical thinking skills are very
important in an engineering curriculum (Douglas, 2012). It stands to
reason that the goals of an engineering education process might best
be met through methods which can be proven to build critical thinking
skills, in addition to conveying subject-specific knowledge. This
implies a need to reliably evaluate both students’ contextual
knowledge and their critical thinking abilities simultaneously.
As recently as 2008, Abrami and his colleagues performed an exhaustive
analysis of literature concerning the teaching of critical thinking
skills. They mainly found that methods which attempt to teach
critical thinking skills are generally successful at doing so. In
particular, they found that students learn critical thinking most
reliably when CT skills acquisition is a stated objective of the
course; indirect approaches, where students are expected to learn CT
as a by-product, are generally not as effective.
There are, however, some important limitations to the current
literature on critical thinking. As Abrami et al. (2008) observe,
“[critical thinking] is a complex and controversial notion that is
difficult to define and, consequently, to study.” Most definitions
take a pornographic (“I know it when I see it”) approach to defining
critical thinking, which is not terribly useful from a research
perspective. On the other hand, the current scientific definition of
critical thinking (as defined by the American Philosophical
Association – Facione, 1990) comprises the better part of a paragraph,
which is nice, but intractable (Anderson et al., 2001). Therefore, it
can be argued that there needs to be an engineering-specific
definition of what comprises critical thinking, and that this specific
skill can be taught in the classroom.