This.Mistake #1 was telling her you weren't sure if she had a good time. That looks insecure and needy. Does not make you appear to be a high value, high status man.
Mistake #2 was telling her she was hard to read. That communicates that you are focused on figuring out if she likes you, instead of figuring out if she is worthy of you (IE you like HER). It gives her all the power and sets the frame of it being her choice whether to accept or reject you. She was likely testing you to see how you reacted to mixed signals and a bit of rejection to assess your confidence and frame.
Mistake #3 is talking about anything political on a date unless you are certain you both share the same politics. So this was you talking about the book. Also another mistake related to this is in your statement that "women prefer to read..." Never say this. Never say to a woman, as a man, what most women do or do not like. Even if you are right, it's just not for you to say. Now, usually only a feminist will get butt-hurt over this but I've just found it's easier and better to avoid these kinds of comments/statements.
Mistake #4 was backing down from your position on the book when she got uptight about it. Never do that. Never change your opinion or try to smooth over a disagreement about an opinion or belief.
Calling her out on hold/cold behavior is also a bad idea. Some things you must deal with overtly (crossing boundaries) and some covertly (more subtle things like hot/cold). The worst thing to do is call out cold behavior because it shows you are insecure and easily frustrated and are hoping she likes you. How would a high status man with choices respond to cold behavior? By moving on to the next girl and not wasting your time. If I was in your shoes on the second date, I would have simply looked at my watch 30 mins into the date and said, "Well it's been fun but I have to meet a friend. Let's head out" and let her hamster spin about who it was I was meeting and why I cut the date short.
She sounds a bit uptight anyway. Probably not worth the effort.
Also, when a woman runs hot and cold, it’s usually because there is another guy in the picture, maybe an old ex. She goes out with you when she is having problems with him. You almost never get sex from these type of women, she mentioned that you were making too much sexual innuendos. A woman who is attracted to you will not tell you this. She will laugh and flirt back. This one is done. Next.