I have posted question that's (in my opinion) very decent, and somebody cast a close vote on it. As I am curious, I would like to know the reason that he selected to request closing my question, and see if I can possibly improve it. Is there a way to discover that?
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When a post accumulates enough votes to close, it is closed. Underneath your post a banner is displayed that says that the question was closed, who cast the close votes, and the majority reason for the closing. The reason is generally a good indicator as to what the voters were thinking when they cast votes.
In your specific case your post was closed for being Off-Topic. Beyond this general reason, there's no mechanism to get a more concrete reason from the voters as to how exactly your post didn't fit with the guidelines. You could post a question in the comments section asking why people voted to close, but this is often though of as unwanted noise, and there's no burden of responsibility on the voters to further explain themselves.
You have a few means at your disposal to figure out why your post was closed.
In your case, the FAQ spells it out pretty plainly in the section "What kind of questions should I not ask here?":
It then lists off several examples of subjective questions that are likely to be closed. Yours is a prime candidate, asking for what essentially amounts to a list of things similar to the first example given, "What's your favorite __?" Questions asking for lists of things are frequently and quickly closed as being off-topic. I agree with the closure in this case. You post was off-topic for SO.