Why are [some] professors ambiguous about material that is actually tested on exams?
There are at least four worries, in my experience:


The students may be trying not to study any more than they absolutely have to study. So if the professor says something isn't on the exam, they won't study it. 
If the professor says what is on the exam, but doesn't explicitly mention something, and then that thing comes up (even as a minor part of another problem), the students may complain that "you said that wasn't on the test!". This can happen even if the professor really made a good faith effort to say what was on the test, and the students simply misunderstood.
The professor may not have written the exam yet, and so she doesn't know the exact topics that will be included.
Someone else may write the exam, if there are many sections of the course taking the same exam. In that case, the professor may not be permitted to say what is on the exam. When I was a postdoc, they didn't even show us the common calculus exam until just before it was administered. 


There are various strategies to cope with these worries. A common one, as described in the question, is to just say that the exam can include everything from the class, which is not very informative but is otherwise harmless. 

There are other strategies, as well, such as making an exam review packet that includes more than the exam possibly could, and then selecting exam problems based on the review packet. But these don't help with the issue of common exams written by someone else.

By the way, if turnaround is fair play: we professors often ask the dual question: why do students so often ask what will be on the exam, when they have just had a class on the same material that will be on the exam?  As you can imagine, we may feel that we have already told the students what we want them to know, by designing the course to include it!