A found that there is a lot of negative attitude towards debuggers amongst academia and seasoned systems programmers. I have come up against one quite talented programmer who claimed that "Debuggers don't work, i just use log files." Fair enough, for multi-threaded server apps you must have logging, but there's no denying a debugger is useful for 99% of the code that is not multi-threaded.
In answering your question, yes debuggers should be covered in programming syllabus, but as one of the tools of debugging a program. Tracing and logging are important as well.