Is the Scrum Master a "manager" in the traditional business sense of the term? No. However, the Scrum Master does in fact "manage" a number of things within the Scrum Framework.
Once you realize the original question is a definitional one, you are forced to accept that the vagaries of both the English language and the test-development process can heavily influence the "correct" answer to a test. What's considered correct is solely determined by the answer that the test's authors expect you to give. Truth or real-world congruence have nothing at all to do with the correctness (for scoring purposes) of the test.
As you will discover below, while the Scrum Master role is not meant to be managerial, the role is designed to manage certain things. Those in a role that manage are managers. QED.
Caveats on Test Design
Test design is largely outside the scope of PMSE, but it's worth noting that most certification tests are normed. Regardless of how they come up with the question, the "correct" answer is the one where an acceptable percentage of test-question beta testers answer the question the way the test writers expect them to.
Trying to parse questions like this for canonically-true answers is largely a fool's errand. However, it is occasionally useful to try and understand what the test writers were fishing for even if the answer isn't "true" in a real-world sense. This means that 100% of the conversation is really about how other test takers likely interpreted the question, rather than what the test designers actually thought. There's no way to really know the latter, so it's purely speculative.
What Other People Think
You say that a lot of test takers believe the following:
The Scrum Master manages the Scrum process. If the Scrum Master is not a management position, he or she may not have the influence to remove impediments. The Scrum Master does not manage the team.
These individual statements are all true, so far as they go. Let's take this a piece at a time in the following sections.
Managing the Scrum Process
The Scrum Master manages the Scrum process.
This is mostly true, once you realize that the primary definition of manage is:
be in charge of (a company, establishment, or undertaking); administer; run.
So yes, the Scrum Master is generally considered by many organizations as in charge of the Scrum process, and therefore (by extension) the project. This is certainly arguable, but it is most definitely common. What is less arguable is that the Scrum Master is a process coach or referee, which means that the Scrum Master administers or runs the process.
Remember the caveats: you can debate the definitions if you want, or hair split to your heart's content, but the normed questions are what constitutes a "correct" answer on most certification exams.
If the Scrum Master is not a management position, he or she may not have the influence to remove impediments.
This is also true. Ask any process owner whether they are more successful in removing impediments through influence or direct/delegated authority, and you will almost always be told that the latter is more effective. Scrum is really no different.
The dictionary provides the following secondary definition of manage:
succeed in dealing with or withstanding (something).
In order to effectively clear impediments, a Scrum Master must have sufficient influence or authority within the organization to effect change, obtain resources, or otherwise affect the source of (or solution to) the impediment.
There's an old aphorism that says "Those who can, do. Those who can't, manage." In most organizations, if you're not a doer you are (almost by definition) a manager or executive, and I don't know anyone who thinks of the Scrum Master role as an executive organizational role.
All people are really saying is that a Scrum Master who is perceived by the organization as being invested with delegated authority to "succeed in dealing with" a project's impediments is going to be more successful in clearing those impediments than someone who is perceived as holding a purely advisory role.
Teams are Self-Managing
The Scrum Master does not manage the team.
In this case, the sentence is likely using the term "manage" in the more formal sense of authority. The Scrum Master has no formal authority over team members, and so does not manage them in the traditional organizational sense of the term.
The role of the Scrum Master is clearly spelled out in the Scrum Guide. The Scrum Team is self-organizing, but the Scrum Master is responsible for (e.g. manages) the Scrum process and enforcing adherence to Scrum's theory, practice, and rules.
The quote about not being in charge of the team is a restatement of an implicit statement about the role of a "servant-leader" within Scrum. The Scrum Master is not in charge of the people on the team, but is responsible for adherence to the Scrum framework.
This is why I generally say that the Scrum Master is a process referee. In football, the referee doesn't manage the teams; the referee enforces the rules of the game. It's the same with Scrum, although Scrum Masters are usually asked to coach and evangelize too, rather than simply blowing the whistle or calling fouls.
The Scrum Master role is not managerial, but it is arguably a "manager" role. So, the accepted answer may be technically (or at least arguably) correct, but it is still wrong in a broader sense if Scrum is being implemented properly.
It's a poor-quality question. Some exams allow you to dispute such questions, or to defend alternative answers. Assuming this isn't one of those exams, just accept it as a poor-quality question and move on with your life.
The real-world answer is that the Scrum Master should be a:
- process referee, and
- framework coach
but is often a traditional project manager or other middle-management resource who is simply flying the agile flag. When that happens, the question of whether the Scrum Master is a manager has more to do with the implementation than the framework.
When one assumes the only two choices are "task performer" or "manager," the Scrum Master's role is likely to be misattributed. The whole point of agile frameworks like Scrum is to help people think outside that very small box...if they can 👉manage it.