"For the record, I am not an admitted homosexual, nor am I a homosexual, though I do know the lyrics to every show tune ever written, which might perhaps account for the confusion"

John Podhoretz is making an amusing declaration about his knowledge of show tunes and how it may result in confusion about his sexuality. He is clarifying that he is not an admitted homosexual, nor is he a homosexual, but he does understand the lyrics to every show tune ever composed. This might be translated as a joke about how individuals may presume he is gay since of his understanding of show tunes. He is also poking fun at the stereotype that gay guys are more likely to know program tunes than straight guys. By making this declaration, he is highlighting that his knowledge of show tunes does not define his sexuality.