The Quiet Man is about a boxer from America who returns to his homeland of Ireland after retiring. There he falls in love with a feisty Irish woman. It was a no brainer to cast Maureen O'Hara as the feisty Irish woman. Playing opposite the quintessentially American John Wayne was the perfect role for her. She was a feisty Irish girl herself.
She was good friends with John Wayne and the two of them worked on many films together. Of course, many of those were Western films. The 1950s were a great era for Westerns. Audiences just ate them up, especially if they starred John Wayne. For many men in the 50s, John Wayne was their example of what a man should be. Whether or not that's a good thing is up for debate.