Everyone has an idea for a story. To dream up ideas is a part of being human. Writing down an idea is what changes you from being a dreamer to being a writer. When an idea is unwritten it is half-real like a dream. Writing it down is the act of creation. Writing is making something out of nothing.
Once you have your idea on paper it might need to be worked on. It might need to be changed and developed or revised. All those things are secondary because the most important and first step has been taken. You have written something down.
So take the plunge, write down your idea! Becoming a writer is easier than you think.