Can Someone Please, Please I'm Begging You, Explain To Me How Maverick Pulling Rooster's Papers From

Can someone please, please I'm begging you, explain to me how Maverick pulling Rooster's papers from the Naval Academy would have pushed his career back four years? I have no doubt that Maverick pulling his papers would have cost him years on his career to becoming a Naval Aviator, of course, but as to how that would have been the case, I'm pretty in the dark. Like, when did he find out Mav pulled his papers? Was it after he turned 23, so he already passed the age where one could apply/re-apply for USNA? But if that was the case, what was he doing in the meantime? It was still his goal to become a Naval Aviator, so what was he doing between 17 or 18 (probably the age he applied) and 23? Or did Rooster learn his papers had been pulled earlier on? But if that was the case, why didn't he just re-apply to USNA? Or am I missing critical details to the entire situation altogether, and completely misunderstanding what happend and the circumstances? I have no idea. I don't even fully know what "pulling papers" really entails. Is it something that anyone could theoretically do, or is it something that could only be done by Maverick because of his military/naval position? I am very confused.

If someone would be kind enough to explain, that would be beyond appreciated!