Sometimes a puzzle consists of various parts, and the answers posted each solve a part of the puzzle. In that case, it might be useful, after the puzzle is solved, to post your own answer that consolidates all of the bits and pieces into one coherent answer.
Similarly, someone may stumble across the solution in a way you didn't intend, or might have missed a particularly-clever clue you provided. You may want to post your own answer that provides your intended solution, even if the solution provided was correct.
So I would say there are some reasons to post your own answer, but generally it would be after someone else has solved the puzzle. That being said, there's nothing stopping you from posting the solution to your own puzzle if you so desire.
People also sometimes post puzzles for which they themselves do not have an answer. If they subsequently solve the puzzle or discover the answer, that could be a situation where answering one's own post would make sense.
Please also note that this site is not just for posting puzzles, even though the vast majority of posts fall into that category. It is also for questions related to the creation and solving of puzzles, and there could easily be situations, much like other StackExchange sites, where you would answer your own question about these subjects.