There's a song by the Beatles A Day in the Life. I can't figure out why that the is there. Would it have been different if it had been written as A Day in Life?
"A Day in the life of (X)" is a very common phrase (it doesn't even need to be a person):
- ATL24 - A day in the life of the world's busiest airport
- A Day in the Life of a Primary Care Doctor
- A Day in the Life of Nike CEO Mark Parker
It could have been A Day in Life, but it adhered to this more ambiguous form here; from whose life was it a day? The man who "made the grade"? It doesn't really matter.
A Day in the Life (of X) is a common enough phrase, it could be anybody.