Everyone is scared to make mistakes, some more than others. What you need to realize is that you're only human. As life goes on mistakes will inevitably happen and you can't control everything. The good thing is that there are chances to make up for them.
To the student that forgot to finish his homework, its okay. Missing one homework assignment won't prevent you from being successful in the class overall. To the employee that accidentally slept in and was late for work, just be careful for next time. No one hates you for being late because it happens to the best of us. If you hurt a loved one, apologize, make amends, and move on. There is no need to beat yourself up over what already happened.
Of course, not all mistakes are the same. Some mistakes by nature are bigger than others but if you know that you made a mistake, it makes you more self-aware which is great for preventing another one. The missteps you make are meant so that you don't make that kind of choice again.
If you think that you're the only person to slip up from time to time, that is not at all the case. No one is perfect (as cliche as that sounds). You should be more worried if you've never made a mistake in your life up until now. The things you do (good and bad) shape you as a person.
Think of it this way: how are you supposed to know not to eat too much candy because it will make you sick, unless you've experienced it before?
