Final answer:
The narrator wanted his bed to be exposed in order to allow whatever was trapped behind the wallpaper to escape, relieving his anxiety.
Step-by-step explanation:
The narrator wanted for his bed to be exposed because he was paranoid and believed that there was someone or something trapped behind the wallpaper in his room. He thought that exposing his bed would allow whatever was trapped to escape and relieve his anxiety. In the story, the narrator becomes fixated on the wallpaper and starts to see a woman trapped behind it, which contributes to his deteriorating mental state.