Your professor makes a good point. The 10,000 gallons of kerosene remaining on each aircraft burned at 1,500 - 1,800°F (800 - 1,000°C). Steel loses 50% of its structural strength at 600°C, and 90% at 1,000°C; more than enough to weaken the towers' frame to the point of collapse.
On the other hand, the fuel actually burnt itself out within 10 minutes; but the combustible interior fittings (rugs, curtains, furniture, paper, etc.) ignited by the initial fire kept burning at extreme temperatures, sustaining the heat transfer that eventually brought the towers down. A plane running on empty might have lead to a much smaller and less intense fire initially, but even that might have only delayed the towers' collapse for a few more hours - the structural damage from extreme impact velocity would remain, the fire would inevitably becomes self-sustaining, and there was simply no way for any firefighting effort to even reach (let alone effectively combat) a blaze between
77-95 floors above ground. And as
@Wolfram have said, the hijackers knew about a high fuel load's effectiveness anyway.
Huh,
there's actually a thread discussing this scenario posted four years ago. It's a more plausible outcome, but I still doubt the WTC complex would survive in the long run: the South Tower earthquake was, by all accounts, too weak to meaningfully destabilise the relatively untouched foundations of the North Tower. It was very much secondary to the weakened steel frame that eventually caused the sagging floors to "pancake" downwards.
United 175 crashing would indeed mean the South Tower’s survival, but the North Tower's collapse would have almost certainly damaged it well beyond repair. The facade would be pummeled by thousands of tons of debris, with secondary fires being ignited across the tower's length (as happened with 7 WTC).
Eventually, the ruined South Tower would have to be torn down; as I've said above, both the economic and psychological impact cannot be understated. Controlled demolitions are banned in NYC for obvious reasons; the only option would be to gradually dismantle the South Tower floor by floor. An unprecedented and immensely costly undertaking, but still less so than the equally unprecedented repair and reconstruction of the towers - which would also lead to far less economic gain, since
who the hell would want to return?
Billions would have saw the North Tower burning and collapsing on live TV, just like OTL; even if no expense was spared in restoring the Twin Towers, would any corporate tenant be willing to put their headquarters at risk of instant destruction? Would any of their employees be willing to live and work where if anything went wrong, they might have to choose between being buried alive and having to jump to their death? Note that a pure repair means that incorporating major design changes, such as the new 1 WTC's
improved security features, would be flat-out impossible. The restored Twin Towers would instantly become a financial black hole and public relations disaster.
The quoted scenario below would probably be the likeliest outcome.