There was added to these causes of offence his insult to the tribunes. It was, namely, the festival of the Lupercalia, of which many write that it was anciently celebrated by shepherds, and has also some connection with the Arcadian Lycaea. At this time many of the noble youths and of the magistrates run up and down through the city naked, for sport and laughter striking those they meet with shaggy thongs. And many women of rank also purposely get in their way, and like children at school present their hands to be struck, believing that the pregnant will thus be helped to an easy delivery, and the barren to pregnancy. These ceremonies Caesar was witnessing, seated upon the rostra on a golden throne, arrayed in triumphal attire. And Antony was one of the runners in the sacred race; for he was consul. Accordingly, after he had dashed into the forum and the crowd had made way for him, he carried a diadem, round which a wreath of laurel was tied, and held it out to Caesar. Then there was applause, not loud, but slight and preconcerted. But when Caesar pushed away the diadem, all the people applauded; and when Antony offered it again, few, and when Caesar declined it again, all, applauded. The experiment having thus failed, Caesar rose from his seat, after ordering the wreath to be carried up to the Capitol

— Plutarch, The Life of Julius Caesar

Some believe the event was staged by Caesar to gauge how much support he would have to name himself king. Had he not received sufficient push-back, he’d have gone ahead with it.