The point is to create a line of least resistance for the punch to follow. It’s not drifting, as the punch is wider than the pilot hole — that is, it does still remove a slug (polo-mint [or Lifesaver, for those of us in the USA] -shaped) and you’re not simply widening an existing hole without removing additional material.
The advantage of this method is that it gives you a little extra insurance that your eye will come out straight. It’s not really necessary, and I’ve punched plenty of eyes without one. However, since I wasn’t firing up the forge yesterday, I thought I’d zip in the holes just for giggles. The steel is not hardened, so it didn’t require any special drill bits or annealing.
Cut all the way around, and finish with a hacksaw if there’s anything left in the middle.