Private browsing will automatically be disabled when you "Limit Adult Content" in your Settings. Here's how to get there. It takes 2 minutes.
1. Click your Settings app
2. Tap General
3. Tap Restrictions
4. Tap Enable Restrictions
5. Create a 4-digit password
6. Type in your password again
7. Tap on Websites
8. Tap on Limit Adult Content
This will make the private browsing option disappear!