Much of whether you should consider a course instructor a manager depends on the type of instructor. Tenured professors (Associate and Full Professors in North America) tend to have more managerial functions than more junior faculty.
In large lecture courses, professors supervise multiple TAs and support staff. Like managers in a business, they assign tasks to their TAs, provide guidelines for how those tasks should be performed, and attempt to ensure successful outcomes.
The shared governance form of university administration means that faculty members have managerial duties such as curriculum planning (deciding what courses should be offered every year, how many students per class, etc), hiring TAs and new members of departments, promotion and tenure decisions, strategic planning for their departments, developing department and university policies and procedures, etc. These tasks involve many traditional management skills in resource allocation, human resource management, work flow management, etc., and are necessary to the functioning of courses, but aren't actually classroom teaching.
The work of teaching courses and doing scholarship is a professional activity, but teachers also have major management responsibilities outside the classroom that are necessary for courses to function smoothly. If you have ever wondered why professors may teach only two to four courses a term, much of the explanation has to do with these managerial responsibilities, which can occupy almost as much of a professor's time as actual teaching.
For the most part a course instructor could be compared to a manager. A manager's roles include planning, scheduling, programming, budgeting, and creating objectives. Each of these roles are seen from an instructor.
At the beginning of your course the instructor provides you with a syllabus. This document declares the objectives of the course, in other words what he/she expects you to learn or achieve.
The instructor also budgets with time and scoring. He/she gives you a total amount of points you can earn for the course. Depending on how well you learn and how hard you work, you will climb higher and closer to that number. An instructor can also withdrawl points for attendence or cheating.
Programming is also used. The teachers builds on the subject. In math you would have to first learn to count, then addition and subtraction, then division and multiplication and so on.
A manager must use each of the above functions and more to complete their job. Skills would include: Patience, good communication, critical thinking, time management etc.