Do you need to have bedroom door open in order to have the central cooling system to work properly?

My Landlord states that i need to keep my bedroom door open in order for the room to get cool. there is an air conditioning vent over the bed. I noticed the room was warm and asked him. he told me there has to be air flow. that the cool air has no where to go. its a cycle that needs to be done with the air.comes in must go out.is this true? wheres my privacy if i have to leave my bedroom door open?