But when you have many tasks that are way past-due, it's more important to just get work done — the tasks are already very late, so if they actually were an urgent priority, they would have gotten done earlier, and letting one task slip a tiny bit more while you finish another task obviously isn't a big deal at this point. Also, trying to survey the larger picture can just make the pile of work seem more daunting than it really is... it's more important to just start moving.
Also, when a person says "I don't want to work on task-A because task-B is a higher priority", sometimes they really mean "I don't want to work on task-A. Furthermore, if you ask me more directly about task-B, I'll find an excuse why I can't work on that yet either". Sometimes we use this to unwittingly fib to ourselves. To prevent this from happening, just ignore priorities when you get very far behind.