Lots of reasons, but to highlight a few:

Internal

• Have a full-time job, don't want to get in trouble with your boss or send mixed signals about commitment
• Still validating the idea, afraid of being embarrassed by friends / prospects who can connect you directly to the concept

External

• On the cusp of something new that a more resource-rich group could pursue without you, therefore you want first-mover advantage
  
• Rare: launch will be more effective if timed strategically (ie: http://Feedly.com pumping ads during Google Reader shutdown)

B2B

• Businesses define needs, then find a product to suit them, then evaluate build vs. buy. If you start stealth and focus on product, you may win more 'buys' and lose fewer 'builds'
• High barrier to entry, MVP not suitable for target segment

B2C

• Consumers are fickle. High bounce rate if product doesn't clarify how it adds value. Private beta's may be the answer to this challenge
  
• Thanks to social media, consumers now have a voice. They define your brand, not you. Stealth can help protect the brand you don't yet have