A friend sent me this Reddit AMA about some dudes starting YAMACYC ("yet another me-too accelerator copy of YCombinator").
I wrote back: "Secrets are stupid in start-ups."
While mine was a flippant answer, my point is that keeping your business idea a secret is the exact opposite approach a founder should take. Instead, you should be telling everyone everything about your idea.
In startups, you want to learn as much about your market as quickly as possible. You want to launch your product as soon as possible. You want experts in the field to tell you what your blind spots are. You want to find out if anyone actually wants to buy your product. (Spoiler Alert: They usually don't.)
So, back to the Reddit AMA. While I applaud this guy for trying to build an accelerator, keeping it a secret is a wrong way to go about it. He's missing a great opportunity to get feedback on his idea and see if anyone actually cares. If they don't, he could save himself a lot of time and work on something else.
Oh, and can someone steal your idea if you tell people about it? The answer is "sure, but who cares?" If your idea could be copied and done better by someone else, it wasn't a good idea in the first place.