Sometimes the hardest thing can be admitting you've made a mistake. It requires you to go against your own ego, which can be our worst enemy. However, failure is the mother of success.
When you fail at something, you are actually one step closer to finding a way that will succeed. We all learn from failure, and when you learn about how something doesn't work, you can eliminate the idea, narrow it down and continue to find out how it really works.
Never be ashamed to fail. Why are so many people afraid of failure? Because failure usually creates a negative feeling, giving us the idea that we aren't good enough or that we've done something wrong. We need to understand that with careful reflection, we can investigate the root of our failures and work towards avoiding them in the future. The more you fail, the better chance you have at success in the future - it's called experience. For experience to work, the most important thing to remember, is to avoid committing the same mistake twice. Otherwise, we are not any better off than our previous experience.