Is it possibly because it is a closed question? Does a question being closed merit downvotes for possibly good answers?
Since the question, and its answers, has now been deleted by the community, here is the answer for reference:
It sounds like there really isn't a lot you can do. I'm assuming you're working "at-will", which means you can leave or be dismissed at any time for no reason.
Going forward, I would send a message to your former manager and ensure you can get a decent reference. If not, the best option may be to write it off.
If they gave you a specific reason that you were fired, you can pursue that. Otherwise, moving on is pretty much all you can do.
If you pursue this, it likely will open a can of worms that will overshadow the job that you just left.
I'm not sure you did adhere to the back it up principle here, as there isn't any information included that backs up any of these statements. I'm not sure I would have downvoted this post or mentioned that it needed statements backing it up, as I generally reserve my comments for the worst offenders. Still, I wanted to point out that backing up an answer would include facts, references, or experiences that happened to you personally. Instead, this appears to just be your opinion or advice. That doesn't mean you're wrong or you don't know what you're talking about, just that there's nothing here to validate these statements and prove that you know what you're talking about.
With that said, I'm not sure whether or not the back it up rule was why your post attracted some downvotes. It could be that it just wasn't possible to give a definitive answer to such a question.
The question was scored -5 at the time of its deletion, and it was never clear what the exact problem was. The asker chose to remain extremely vague, stating he/she had a problem with a person named "Q" but never really giving us enough details or context to understand what that problem was.
The Workplace isn't a place for hypothetical or anecdotal questions; instead, those about real, actual problem tend to work the best because it takes the guesswork out of answering. As a result, I think it would have been extremely difficult for anyone to give a solid answer to this question because there just simply isn't enough information. Of course, this doesn't mean a hypothetical situation can't be asked here, it just needs to contain enough detail to where we don't have to make up stuff in our heads in order to answer it.
Thus, it's possible the answer received downvotes not because the question was closed but because it's difficult to give a solid answer. However, more people thought your post was helpful than not helpful, considering it's positively scored. As Yannis mentions in his comment, downvotes are pretty common here.
I think you did the best you could to answer the question, but perhaps it would have just simply been best to vote to close. Since the post is now deleted, all rep changes, both upvotes as well as downvotes, have been refunded back to you. Hope this helps!
I sometimes will downvote answers posted to questions which are fairly obviously questions requiring some serious work, especially ones which are rantish or "tell me what to do please."
That being said I didn't vote on your answer either way but have expressed my thoughts on when downvoting answers is appropriate previously.
Your answer had a tone of opinion and provided no objective evidence, and offered no solution which I would consider helpful. And most importantly the answer was not "Expert Quality".
I know that many of our questions do not require the answerer to be an Expert. But when I read a good answer I should not be able to tell that the person answering is not an expert based on how the answer is written.
The answer you provided would be at home more in a chat room than here on SE. These type of answers create noise and act as broken windows causing other people to think that they can post the same type of low quality answer unless we deal with them. As a user the only way I can deal with it is to down vote.
I did not comment on my down vote there because I did not have any suggestion about how to improve your answer, other than to hit the delete button, which would be more likely to generate more comments, something else I Wanted to avoid.