Holding firm to a position is admirable, until it becomes clear that the position is wrong. Those who can admit that they were wrong are able to move forward. Those who stubbornly claim they are right, in the face of clear evidence to the contrary, become stuck in the quagmire of their own pride. To achieve excellence you must be willing and able to admit your mistakes and to change your opinions.
Mistakes are damaging enough on their own. There's no need to compound the damage by holding on to them. The best thing you can do with a mistake is to admit it and learn from it. The worst thing you can do is defend it and continue it.
Mistakes can be great teachers. Mistakes are inevitable. When you attempt to achieve anything ambitious, you are certain to make some wrong turns. Yet even those wrong turns can move you forward if you have the courage and humility to admit you made them and then turn back from them.
Whenever you're making progress, you're also making some mistakes. Spot them, admit them, learn from them, make a course correction and then move yourself ahead faster than ever before.