I am worried that the rep system is leading to careless moderators coming into power. Part of my answer was:"What is unclear to me is whether someone like you who feels somewhat unsure is even less likely at all to graduate with a PhD than someone who goes in thinking R1 Tenure or death. Your waffling MIGHT even be a sign of mental health is what I'm getting at." The deleting mod's comment concerning this passage shows a lack of reading comprehension, which is almost assuredly due to carelessness rather than lack of intelligence: "Suggesting that someone who is not sure if they want to do what it takes to get a PhD might have mental health issues is over the top." I clearly said mental health, a positive attribute, but he deleted my answer from a careless reading, perhaps done due to the dissenting nature of my answer. What can we do to encourage mods not to delete things they haven't really read, and to encourage the promotion of people to power based on quality, not quantity?
I was the moderator who deleted this answer, and after reading the different points here, I agree with the reversal of the deletion, and I'm sorry, I indeed assumed it was offensive.
To answer your point of "careless reading", I actually read your answer, but let me go through the different reasons why I took it at the time (if only to show that we don't randomly delete posts).
It's hard to see how you answer the question. You mention "On the ethical question, I think you have to ask that to yourself and find what your moral code is (I am a nihilist)", so basically, you answer by saying that the OP should answer him/herself. The fact that you personally are a nihilist is particularly irrelevant here. You said in the comments that you expect the same care than in academia, well, we expect the same in answers. Any good, constructive, motivated, justified answer is welcome here, how dissident or controversial it can be. As far as I can tell, the answer you provided is rather a subjective comment than an objective answer, and I'm not convinced how it can help the OP in any way.
Your tone is quite pedantic, especially at the end: "someone like you who feels unsure is even less likely at all to graduate with a PhD than someone who goes in thinking R1 Tenure or death", or "I'd say screw it and act rationally, take what I could.". It is hard to convey a tone on a website, and so it is not necessarily clear whether your tone is motivating or just condescending. In this context, reading "mental health" was indeed perceived as something negative.
At the time of the answer, you basically just joined the site, and you had no reputation at all, and although, ideally, it should not matter, you also have to understand that quite frequently, we have people coming to the website for the only sake of insulting other people, vandalising the site, etc. They usually take anonymous usernames and have no reputation. Hopefully, you shouldn't see much of them, since we try to remove any offensive content as soon as possible, but unfortunately, your profile at that time could have been easily categorised as such.
The different points above led me to believe that this content was offensive, and should be deleted, which was supported by the fact that the answer was flagged. It was a mistake, but I wanted to clarify why I took that decision. Deletion can be reversed (and as a matter of fact, it was), so I'd rather delete content interpreted as offensive, and clarify things later, rather than letting it linger.
I'm glad to see that the process is working, and that you came to the meta to protest about it, which is the correct way to handle it!
While a diamond mod cast the final vote, I cast the first delete vote and threw the flag. As soon as I saw your edit, I threw another flag saying I was wrong. I also left a comment so it would be clear why I was voting the way I was. I would have voted to undelete, but I am not allowed to vote to undelete diamond mod deleted answers. I checked back soon there after and the answer was restored. If it hadn't been I would have followed up in chat/meta to make sure it got taken care of. Once the answer was undeleted, I added a comment apologizing for the mix up.
Having an answer downvoted/deleted can clearly be off putting to a new user. Having an offensive answer (or even one that can be easily misread as offensive) is also offensive to new users. The nice thing about the SE system is that we can fix screwups. The voting and flagging systems can fix most problems and the chat and meta systems can help with the difficult issues.
Let me preface these comments by saying that they are an attempt at explanation, not excusing behavior. Your answer was fine, but I could also see how it could be misconstrued, because I did the same thing as the other voters.
Looking back at the history of the question, the issue is that you went back and added the section about "a sign of mental health." It might be a minor thing, but I read that question and had a similar reaction to the users who voted to delete the question. (Note: a mod cast the last vote, not the only vote. Multiple votes were cast to delete the question, so more than one person had the same issue.)
While your sentence is perfectly reasonable, writing "a sign of mental health," the almost-Pavlovian instinct is to mentally tack on "problems" or "issues." The votes to close came following the change (obviously), and I can see how they came about. But, as eykanal mentions, what you've done is the right way to do this.
Using my Super Sekrit Mod Tools, I can assure you that this is something that happens to everyone; old mods, new mods, red mods, blue mods. While I wasn't involved in this particular questions, there have been questions I closed due to my skimming the question and not getting the nuances. If I would ask about this in the mod chat room, I doubt there would be a person there who hasn't done this themselves, probably more than once. Your response—posting a well thought-out, not too accusatory post on meta—is the appropriate way to deal with this, and I really commend you for it.
To that extent, after reviewing the flags and the discussion, I've undeleted your answer; I can't see any reason why it should have been deleted. For what it's worth, the answer doesn't really directly address the question, so you may want to consider either revising to make it more directed to taking a different direction with the answer. However, your point about the unfairness in deletion makes sense to me.
If anyone has issue with this undeletion, please post in the comments below this answer so I will receive notification of your comment.