Nicodemus didn't make a mistake...He knew that to be born from above meant to be 'born again'...And he quailified this statement by referencing the fact that how can he be born twice from his mother's womb...
I don't understand your problem with the word 'again'...
From the context Nicodemus understood Jesus to be saying “again” as in a repeat and hence a Greek word, anothen, was chosen to translate what Jesus said.
A simple statement, “born again”.
Thayer’s Greek/English Lexicon might be helpful.