Ideas are cheap. No young writer likes to hear this, but it's true. No one is going to steal your idea, because most of us have so many ideas already floating around in our heads that we just don't have time for yours, thank you.
Of course, even if we did, the story we'd write would be totally different from the story you'd write anyway. But even so, what's far more likely is that your idea would give us an idea, which would probably go off in a completely new direction and might eventually become quite unrecognizable, as far as your original idea went.
Still, it's hard not to get protective of your ideas and want to keep them to yourself. I'm not sure if that's because we're really truly worried about "theft," or if it's more that we're afraid the idea won't sound as good outside our heads as it does inside. Because of course the idea in your head is full of nuances and images and backstory, far more than you can hope to convey with a short description that probably sounds kinda lame. And who wants to work on a lame story? I think what we're really worried about is stealing our own thunder.
Image: Bright Idea by Zaldy icaonapo