Making excuses can be a polite way to decline an invitation. Other than that, it is a smart choice to avoid making excuses.
Why is making excuses bad? Not only it reveals other people a lack of backbone, but it actively prevents growing one.
Making excuses to others is a minor thing; making excuses to yourself is a terrible crime. If you failed and learned from failure, don't dwell on it anymore - look forward to failing again! If you make excuses, you are basically saying to yourself that you don't have the willpower to try anymore; to prevent failure, you choose to give up altogether.
Of course, there is a difference between making excuses and providing explanations. If you are providing an explanation, you are assuming responsibility and facing the consequences. (With an explanation at hand you can analyze, and by analyzing you can learn.)
If you are making an excuse, you are not accepting responsibility and not facing the consequences. You are looking for a scapegoat, whether it be an action, a thing, or a person.
Nothing destroys a person from within more as the choice to constantly make excuses - it is a shortcut to unhappy life and poverty.