[justme]

The very simple explanation for this is that the departure time is exactly that, DEPARTURE time. It's not the time they close the boarding door, it is the time that the flight is supposed to be pushing back from the gate. There is quite a bit of paperwork that has to be printed, and then the flight crew has to do some calculations for weight and balance and input it all into the airplanes computers. That is why the stop boarding 5 - 10 min (depending on the airline) before departure time. It gives the gate agent time to print everything, the pilots time to do their calculations and input them, and the FAs time to get everyone seated and their stuff stored. By the time all of this is done, the door is closed and the flight leaves on time. If they waited, even for just one passenger, this whole process would be delayed resulting in the flight being delayed. Yes, I agree it sucks that you missed the flight and were 4 hours late, but do you think it would have been fair to the other passengers on the flight to delay them to wait for you? It's a matter of weighing the benefits and consequences to delaying the flight. One unhappy person is not as bad as potentially hundreds. Hope that helps you understand why the doors are closed several minutes before the departure time listed on your boarding pass.