The FAQ entry you quoted for question deletion guidelines doesn't actually say anything substantively different from the guidelines on question closure.
Despite the fact that some users had voted up your question, a significant number of different users (and presumably those with higher reputation as required to attain close-vote privileges) considered it to be off topic for this site and closed it. Specifically, it was closed as "not constructive", which is officially defined as:
This question is not a good fit to our Q&A format. We expect answers to generally involve facts, references, or specific expertise; this question will likely solicit opinion, debate, arguments, polling, or extended discussion. See the FAQ.
Closure has multiple purposes.
The first one is relatively temporary: it allows the community to convey to the person who asked the question that there is a significant problem with it, provides them the opportunity to correct those problems (and, if necessary, elicit help from the community in the comments in order to aid them in correcting those problems), and then subsequently have the question re-opened. The reason why it gets closed in the first place is to prevent a flood of answers that will become irrelevant once the question is substantially overhauled to bring it into compliance with guidelines for the site. Rather than a moderator deleting all those perhaps well-intentioned but now irrelevant answers that accumulated before the modifications were made, the question is simply closed to prevent answers from accumulating in the first place. In other words, you can think of this use of closing as a signal to the asker and a block against new answers that will quickly become obsolete.
The second purpose is a bit longer term. In this context, closing is a gateway or first step on the road to deletion. The idea is that we don't want questions that are off-topic or otherwise don't fit within our guidelines to be hanging around on the site. Somewhat akin to the broken windows theory in criminology, the idea here is that the presence of high-quality questions will encourage others to ask high-quality questions, whereas the presence of low-quality questions will prompt others to assume that such questions are acceptable. The Q&A sites that have been running for a very long time (such as Stack Overflow) are a great place to see this theory in action. If off-topic questions are not closed and removed under the theory that they might be helpful or interesting to someone, you have a bunch of other users justifying their own off-topic questions under the rubric of "I've seen lots of others like it!" Then you get a lot of complaints on Meta about the site's guidelines being arbitrarily and capriciously applied.
With respect to the cited question, it was closed and you went through the first phase, but nothing happened. There was no attempt made to edit or revise the question, it just sat there. Referencing the above analogy, it was a "broken window" in need of repair, but receiving no attention. It hung around for around 60 days without any activity or interest. I think that's quite long enough to give you ample opportunity to revise it. In addition to the lack of activity on the part of the asker, there were no votes cast to reopen the question by any other members of the community, indicating a general consensus with the decision to close it.
Thus, it proceeded to phase two, with closure acting as the gateway to deletion, and was subsequently removed.
Beyond that, you left the following comment on February 4th in response to a prompt by a moderator to (again) consider editing or revising your question:
Kill it. I can't think of any way to describe it better. I'm sure now the truth is much simpler: once the communication is in context, the anti-position is derived from context, and the more basic explanation is "non-cooperative communication". My fallacy theory was a red herring of over thinking the problem, or the naive assumption someone had described the problem in more detail to bestow it an -ism. (>_<)
I interpret "kill it" as an instruction to delete a now obsolete and useless question, one that you have no intention of (or ability to) revise and improve. What were you expecting to happen differently?
I think all users who participate in good faith deserve to know, How long after a post is closed before its removed? Is there a policy for leaving closed posts on the site?
There is no hard guideline for what I'm terming the second use of closure. Stated differently, there is no set timeframe for how long a question should remain closed ("in limbo") before it is ultimately deleted. But I personally think 60 days is quite long enough, especially given no progress was made towards editing or revising the question.
However, I am upset to find the post removed. Simply put, I didn't copy the discussion and now have no record of the responses. I only have my original question.
No worries, the only answer you received was someone posting a link to Wikipedia about hasty generalizations. That wasn't much of a motivation to preserve the question, either.
I feel like I let someone a book and they threw it out.
That's not really an apt analogy for how this site works. You're not really "lending" anything out. In fact, it's probably more the case that questions and answers exist primarily for the benefit of other users, rather than the individual who asked the question in the first place. The fact that they were able to receive a good answer is more of a happy coincidence (albeit an important one!) of the system. Questions that are unlikely to ever help anyone else in the future are prime candidates for deletion.
Besides, I don't recommend telling the person you loaned the book to to "kill it" if you are hoping they'll give it back.