Why do I have to explain why the answerless, different question is not the answer to my question that has a good answer?
Well, your question is not currently closed as a duplicate, so you don't have to do anything at this point.
What happened is that one person voted to close your question as a duplicate of the earlier one. This is nothing to get worked up about. Just because one person thinks a question is a duplicate, doesn't mean it is a duplicate. There's a reason it takes five votes to actually prevent new answers on a question; there needs to be a consensus of sorts to cause such direct action.
That being said, one duplicate vote does mean that one person didn't understand what makes your new question different from the earlier one. I'd take that as motivation to edit your new question (or, in this case, the earlier question) to make it more clear how they are different. Again, you don't have to do so, but if you don't, you may be passing up on an opportunity to improve your question.
TL;DR It's just one vote, don't worry about it, and I don't think anything needs to be done about this, but consider using the feedback to improve your question.
P.S. I'm sure somebody is going to object that moderators and gold badge holders can close questions as duplicates unilaterally. That's a bit different because mods are "trained" to be conservative about unilaterally marking duplicates; we're aware that just because we think something is a duplicate doesn't mean it is, and so if it's not an obvious case, we often defer to the community. And gold badge holders are expected to have a really good intuition about what questions are really duplicates, due to their extensive experience in the tag.