I asked about the experience that other programmers had about a specific programming language, a question that really makes sense. But I was immediately downvoted with no explanation. Is this a correct behavior for Stack Overflow? It is certainly not very useful. Could you explain why?
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Because it is off topic.
From the faq:
What kind of questions can I ask here?
Stack Overflow is for professional and enthusiast programmers, people who write code because they love it. We feel the best Stack Overflow questions have a bit of source code in them, but if your question generally covers …
… then you’re in the right place to ask your question!
What kind of questions should I not ask here?
You should only ask practical, answerable questions based on actual problems that you face. Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page.
The question in question is way too open-ended and is asking for a discussion. There is no clear way to select a "best answer" and it is going to be begging for an argument about pros and cons of F# vs. whatever other language anyone who stumbles across it may have used. StackOverflow is for specific programming questions, not generic "tell me what you like about it" type questions. Maybe that's more on-topic at http://programmers.stackexchange.com, I'm not sure, but you should read the FAQ for both sites to be clear on where to ask what type of question... though the Programmers FAQ clearly states that questions involving "what language you should learn next, including which technology is better" are not welcome, and the StackOverflow FAQ says something similar about open-ended Qs.
EDIT as requested by OP, after asking if a question is likely to be closed if it can't have objective answers:
That's probably a major part of it, yes, but moderators are of course free to implement rulings based on their individual interpretation of both the FAQ and your question.