Cortana: They let me pick. Did I ever tell you that? Choose whichever spartan I wanted. You know me, I did my research. Watched as you became the soldier we needed you to be. Like the others you were strong and swift and brave, a natural leader. But you had something they didn't, something noone saw but me. Can you guess? Luck.
Master Chief is the perfect hero. He is the living incarnation of hope and humanity.
The Duke is an overly macho tool. Sure he is funny and fun to play as, but he is an Anti-Hero. In general Anti-Heroes suck. I'm going to save the world even though I treat the world like crap/don't care about it... what a storyline.
Oppose that to Master Chiefs story. Humanity has lost every single battle against the covenant. Planet after planet is being glassed leaving billions dead in the wake. Extinction is all but assured for humanity. All of a sudden a story pops up in the front page of the newspaper. Victory. That one word changes the resolve of the entire human race, and gives humanity that most important of emotions. Hope.