Debugging skill is generally useful, even outside of programming. You need it to fix a car that won't start, or to fix a toilet that won't flush, or to figure out why your bread recipe isn't rising well in the oven, or to understand why you fall off a boulder problem at the same spot on every attempt. However, it would be hard to teach debugging independently of another subject, as a general skill. Debugging relies on working knowledge of a system; you need to know a bit about how something works to figure out why it doesn't work. Moreover, debugging requires self-direction and creativity. Debugging is a skill that can be learned, but that cannot really be taught.
Debugging skils are generally useful, even outside of programming, because they are general problem-solving skills, applied to a problem with a program.
I doubt that they cannot be taught, but if that is so, then it would seem that programming cannot be taught either, as debugging is a necessary part of programming. While debugging may require self-direction and creativity, it can hardly need more than that needed to come up with a working program, starting from nothing more than a goal.
The more interesting question is how is it possible to teach someone programming (or digital circuit design) without instilling an ability to debug? If classes are churning out programmers who cannot debug, can their graduates really be called programmers?
I think it can be taught, but it takes a curious character.
Classses are already churning out plenty of non-programmers. Computer science has become famous for being a "sure job". If that is your motivation for entering university you probably never had the necessary curiosity.
