I'm not in the biz so I can't say for sure, but my guess is that they were contractually obligated to turn all those 300-level seats over to Ticketmaster for resale? Or maybe technically they had already been turned over (but SU knew they'd be flipping them as we got closer to the day of the game)?
From the university's perspective, the incentive is two-fold and boils down to the usual suspects: (1) image and (2) greed.
(1) Image-wise, they want a "sell-out" and will juke the stats to claim that. That seems to involve selling large numbers of tickets to Ticketmaster or other brokers, claiming that they're "sold" while understanding that they're not actually yet in the hands of potential attendees.
(2) This practice allows SU to hedge against the possibility of getting stuck with unsold inventory should circumstances change after that bullish summer of season ticket sales. (Say, SU is selling tickets at a steady clip but has always faced an uphill battle filling a 50,000 seat stadium, then demand falls off a cliff when they get blown out in one of their first two games. If they managed 100% of the seats themselves, they're forgoing a bunch of revenue; since they shifted the liability to the brokers, SU makes its money even regardless of demand. Prospective buyers are shut out.)