I had always interpreted HALs actions as he had come to a most curious solution: he had to "complete the mission" but he couldn't let those humans awake know of

I had always interpreted HALs actions as he had come to a most curious solution: he had to "complete the mission" but he couldn't let those humans awake know of the mission. This can be accomplished by having an "empty set" of human beings. To arrive at the empty set involves humans dying, which then sets him up for his further actions (in inactions, in not opening the pod bay doors). This is the conflict which causes his breakdown. So, partially, it was a failure of the people giving the orders that an empty set solution might be the one HAL arrived at: no crew, no crew to keep secrets from.