I've heard all of the reasons for keeping your start-up a secret and I see how some of those reasons weigh heavily on the mind of a would be founder but ideas are a dime a dozen. Everyone has their own ideas, why would they steal yours, especially before you prove it is a good idea. I had a professor at Columbia who advocated for the opposite of stealth. He told founders to share their ideas with as many people as possible and here's why:
1. Don't waste time on a bad idea. If your idea is flawed, better to find out before you spend a bunch of money and time working on it.
2. Social diligence. By talking about your idea you are likely to find out what people might want from a product or service like yours. The more feedback you get, the more likely you are to launch something with real value.
3. People know people. In sharing your idea you are likely to hear things like: "That would be a perfect thing for company X to use" or "My friend might be able to help you bring that market, you should call him" or "I know a guy who failed at a similar project. You might be able to learn some lessons from him".
4. Ideas need to be refined. There are hundreds (thousands?) of ways to present any idea, no matter how simple. The more you talk an idea through, the better you will understand how to present it. You may find that certain audiences react to one type of presentation while another finds that pitch uninspiring. Get to know your audience and how to talk about your project by pitching to different kinds of people with different needs and backgrounds.
These are just a few of the reasons why I am always talking about projects. Even between start-ups I talk about the ideas that are percolating in my mind and taking shape on my white board. unseat.me went from spark to web app after talking to dozens of other ticket holders with similar challenges- too many tickets and no good way to share/promote them to friends. When it seemed clear that there was a need for such a service, I called the likely competition to ask them to build it. I wanted the service and if they were going to build it, I wasn't. But, it wasn't on their product road map. So I decided to proceed. I never would have known that social was not on their road map unless I talked about it. Sure, that might change, but not because I told them I wanted it and not because I decided to do it.
Keeping quiet is a great way to avoid embarrasment but talking about your start-up is so much more useful. Air it out.