When a volcano erupts, why is it that some airlines cancel flights but not others?

It depends on where the flight is heading and if they will be flying through the ash. You do not want an airplane to fly through volcanic ash. There was an incident where an British Airways 747 flew through volcanic ash and all 4 engines stopped. Then got lucky after they descended and the engines started back up. Air Crash Investigations put together an episode about this incident. The episode is called St. Elmo's Fire.

If the destination the flight is heading will fly through the ash, the airline will most likely cancel the flight. If the plane can fly around the ash and not be affected by it, then the airline will not cancel.

Mt Raung in Bali, Indonesia erupted recently. It is near the city of Denpasar, and some airlines cancelled flights, leaving many holidaymakers stranded. But other airlines didn't cancel. Either it was safe to fly and the airlines that cancelled flights were being unduly cautious, or it was not safe to fly and the airlines that still operated were being reckless.

Please note that I am NOT asking why flights are cancelled when there has been a volcanic eruption. It is because the ash emitted by the volcano interferes with the operation of the plane's engines. I am asking why some airlines cancel flights and not others.

It depends which way the wind is blowing the ash.