Why does the playboy in Synge's Playboy of the Western World appeal to us?
I don't think the playboy, Christy Mahon, in Synge's Playboy of the Western World does appeal to "us." At least not by the conclusion of the play. But I also don't think that is the issue you're really concerned with. At issue isn't whether Christy appeals to our contemporary audience, or even Synge's contemporary audience. The issue is: why does Christy appeal to the other characters in the play? Christy gains notoriety because it is thought that he killed his father. As the Widow Quin says, referring to Christy being left alone with Pegeen: "There's great temptation in a man did slay his da, and we'd best be going, young fellow;..." The characters in the play treat Christy like a hero because he has committed this violent act. These characters, by implication, represent Irish society. Thus, Synge's contemporary audiences resented the play, because it suggests they were as oriented to violence as the play's characters. You should be asking why the playboy appeals to the other characters in the play, rather than why he appeals to "us."