Learn English – “No authority” vs “Not authorized”

The issue of plural/singular aside, the phrase, "Two wrongs can't make a right" means that it is wrong to make a second error (usually an error in judgement) to try to cover up or "fix" the consequences of a first error.

An example: Against the rules, a child eats all of the Oreo cookies while his parents are out. The cookies are gone, the first "wrong" has occurred. The kid can avoid a second "wrong" by admitting what he has done and accepting the fact that his parents are going to be upset with him. That would be the smart thing to do, the first mistake has already been made, it's too late to make it better. But, our kid isn't too bright. He tries to cover his tracks. There is a grocery store next door and the parents have a jar of change in the bedroom. The kid steals a few quarters, goes to the grocery store and buys a new pack of cookies. He replaces the cookies he has eaten and thinks all is now well.

Maybe he'll get lucky and get away with it. But two wrongs can't make a right. Even if his parents never catch it, the kid has stolen from his parents. He has now committed a worse crime to try to cover up his first, more minor, transgression. That's usually the case, a second mistake made to cover up a first mistake is usually the worst of the two mistakes.

Too bad he left the empty packages of Oreos in the trash. :)

The preferred formulation is: "You need to believe in yourself and not give up after the first failure." The formulation with "not to" is also accepted.

Here are a few examples found "in the wild" (emphasis added); the last example uses "not to":

• '"You must believe in yourself and not listen to too much negativity," she says.' (Glamour Magazine)
• "At a time when they could have felt under enormous pressure, he made them believe in themselves, and not be intimidated by the challenge." (Executives Online)
• "The theme of the book is to encourage people to stand tall, believe in themselves and not let people around you control the way you live your life." (Michael Panckridge)
• 'Her inspirational message to “any woman who has ever been put down”, is to believe in themselves and not listen to the naysayer’s. In her message she admits “not listening to any of it”, when she was told discouraging opinions by people close to her.' (Go Ask Mum)
• "We should sponsor entrepreneurship as PayPal co-founder, Peter Thiel, has done with his “20 Under 20” initiative, encouraging smart youngsters to believe in themselves and not to fear failure." (The Telegraph)