See this New York Times article about people getting killed for singing Sinatra's "My Way" in karaoke bars in the Philippines. Imagine bars banning this evergreen karaoke favorite. I hadn't really pondered how arrogant the lyrics really are.
In the U.S. we understand the song to be a distillation of Sinatra's "cocky little guy with friends in the Mob" public persona and his leadership of the Las Vegas-based Rat Pack. We also understand that in order to do it "his way" Sinatra worked very hard; he earned the right to make the career decisions the song celebrates.