I was curious why does it permit users to close their own question. What is the rational behind this? Is there any reason a user should be allowed to do this?
On the traditional Q&A sites on the network, the question asker has a problem in mind that they are trying to solve when they ask their question. When another user casts a close-as-duplicate vote, the OP is given a dialog to close the question as a duplicate that says, "Yes, [the dupe target question] answered my question". This makes sense on Q&A-oriented sites.
On the non-Q&A sites on the network (PPCG, Code Review, and Puzzling), the situation is a bit different. Posters don't have questions that they need answered - they have challenges to pose to the community (PPCG and Puzzling), or have working code that they want feedback on (Code Review), so the wording on the dialog is less than ideal. In a perfect world, on these sites, the OP's vote would not weigh any more heavily than the other users' votes. Unfortunately, the Stack Exchange team is unlikely to make those customizations for just three sites, so we have to live with the current system.