Found mistake in my professors book: Tell her or publish? If so, how? 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).
First: Slow down.

In the academic world, books are simply collections of known things presented in a unified fashion. In fact, in some disciplines, it's almost unheard of for someone to release something novel in book form. Additionally, while book chapters are reviewed by editors and (occasionally) peers, it's not the same peer-review setting as we have in journals. To that extent, people don't typically write papers rebutting an interpretation put forth in a book; they write papers rebutting the article(s) upon which the book chapter is founded. If a book chapter does indeed contain an error, then it'll just have to be fixed in the next revision, if there is one. As such, your concern about publication is probably far overstated.

Secondly: Are you sure you have found an error? Has anyone else reviewed your work to validate what you've seen? Are you sure that you fully understand the topic? If I was a betting man, I'd place my money on the professor who's been studying the field for years and has (presumably) thoroughly reviewed the literature, so much so that they just wrote a book on it, over first- or second-year graduate student, as a simple matter of statistics.

Thirdly: You should definitely just go talk to your professor and ask her, respectfully, to clarify what she wrote. If anything, she'll probably be appreciative that you're going through it in such detail. If you have found a real issue, you'll make her aware of it, and if you're lacking some background she can explain it.