I just came across quite a big problem for an interpretation my professor puts forward in her recently published book (a book containing original research in the humanities, not a textbook). I am not 100% sure, but I am pretty sure that I am right.
The error is not a factual error, but an error that concerns the logic of her argument. If somebody interprets a text, and I find very strong inconsistencies in this interpretation or a logical error even, this might not be objectively wrong per se, but it can come close to it in certain cases.
How am I to approach this? Shall I send her an email, explaining everything, or shall I try to publish it as a paper (assuming I am right about the severity of the problem)? I am worried that if I tell her, she might publish a paper herself or will tell me it's not so severe. I am bit paranoid here, I know.
I am also concerned with how to tell her - if I do. Shall I be confident and explain that I think I have found a problem for her interpretation or is this too bold? Or shall I formulate it more like a question? In the latter case, I am worried that she will not realise that I did really see the mistake and am only being polite. I don't want her to think that I pointed to something by asking a question, but that then she really came up with it. I have the feeling it would make more of an impression, if I would point straight to the problem as a problem. Of course, there is then also the possibility of her not liking me for this.
By the way, I am a Master student in the humanities. I will not do my PhD with this professor (or even at the same uni).
No, you won't make an impression by being bold. You are a Master student and she is a Professor, even if you are 100% sure of what you say, you can't just throw your arguments at her face: because you have to show her respect, even if what she wrote is blatantly wrong.
The best way is to point it out as a clarification question, like:
I don't understand this point, because it seems to contradict with [what I have read in another book ; what we know about the organization of this particular structure ; with the latest research ; etc.].
In addition to not being bold, this approach has the benefit of allowing you to present your arguments point by point without seeming like you are arguing (you are trying to clarify a point you don't understand, so you can continue until you clarify it enough). And if it's your mistake, then you will learn something and you can go away without being tagged as a "smart-ass".
I used this approach on several occasions, and it always worked wonderfully well, and even opened a few opportunities (because it looks like you are pretty interested in the subject, which is probably true since you could spot an error).
And remember that making mistakes is easy, particularly when writing a book! So don't be too harsh on someone just because a few errors slipped in: this is bound to happen. However, if the book is full of errors, then you have another problem: do you really want to work with someone that is clearly incompetent or delusional? In this case, you don't need to point any error, you should just get out as fast as possible!
/EDIT: after OP comment clarifying that it is about a substantial reasoning error in a theory and not just a factual error: you can of course discuss with the professor, but be prepared that the debate can become heated. And that's totally normal and you should understand it: she studied the field for years, spent a couple more years to design her theories, and you think you can break her theory at your level of knowledge and study. Of course, this is possible: it is always easier to find a counter-example than to define a new theory. But remember that she put a lot of work in her theory, so even if the theory is wrong, you have to respect her for her effort in trying to advance the research in her domain.
Now you are free to either talk to her or publish a paper, it's your choice, but be sure to respect the person behind the research: as a researcher, your goal is to rebuke/confirm hypotheses and theories, not attack the person designing them. Focus on the content rather than the person (forget about trying to impress), and you should be good.