Most likely no economy seats were available and the airline sold him a first class seat instead. Why should the airline overbook economy class if it can also charge for a first class seat?
If no economy class seat is available, a business or first class seat automatically becomes the cheapest option for lack of cheaper alternatives.
It was actually a simple round trip, and the itinerary with the first class segment was cheaper than other all-economy itineraries on the same and other airlines. Since he was only looking for the cheapest ticket, not specifically for first class (which he did not even realize until checkin time), the airline could have offered the same fare as an economy ticket and still made the sale.