If you just watch the movie then it is not explained why HAL kills the astronauts. It is explained in the later books.
The computer was built to always give the answer to the best of his knowledge and never lie to humans. For this space mission he was given instructions to keep the purpose of the mission secret compartmentalized information because the sleeping ones were the ones knowing the real mission and wake ones were lied to.
It was conflicting instructions, but as long as Dave and Frank didn’t ask questions then the computer didn’t get too conflicted. Things started going awry when the crew did start getting curious.
HAL figured the best way out of the conundrum is to kill them all as dead men don’t ask questions.
Thank you. Was wondering that.
What I wonder about is by shutting down Hal, who ran the ship how would that affect the ship? Wouldn’t it be detrimental to it’s efficiency? Even to it’s stable operation?