Why would the Pakistan airspace closure cancel flights not headed to Pakistan itself?
To give an example of how flights can be affected by this in ways to make them impossible, Iranian airspace is closed from sunset to sunrise (unless things have changed recently).
Any aircraft that due to the closure of Pakistani airspace would need to cross Iranian airspace and be unable to do so because of that closure now needs to be cancelled or rescheduled.

Also, if the diversion around Pakistani airspace would stretch the endurance of an aircraft beyond what fuel it can carry, it cannot fly the route.

Or the diversion would cause such a delay in the schedule that it causes too much problems with the overall scheduling of the airline. Such things tend to have a ripple effect. One flight gets delayed by several hours, dozens of others get delayed as a direct result, hundreds more can suffer delays in the end.

Also, some airports only operate during daylight hours. A diversion around Pakistan might mean the flight can't make it to one such airports before sunset and thus can't land at its intended destination. Now the airline has 2 options, divert to another airport, arrange for bus or train transport for all the passengers, and in the morning yet another hop to the intended destination to pick up the new passengers, or cancel the flight.