There is another reason for delays.
It happens that airplanes have to wait forever for their pushback. The push-back-car is on the stand and waiting.
It is waited until all, really all other taxiing planes have pass this stand.
The blue plane is the one with the delay. Boarding was completed around 04:10, the push-back car was already there. All red-circled aircraft are being serviced. One did not even land. It is now 04:35
OR the delayed aircraft being given a higher priority to taxi based on the severity of delay. This would stop other close-by aircraft on the taxiway to stop and allow the delayed aircraft to proceed for take-off.