If a cat has a distant and aloof personality even within its own home, imagine how remote it would act in a strange place. The expression describes a shy, timid person who is not at home in his surroundings.
A: Asobi ni kiteiru Takahashi-san no tokoro no Masao-kun, tottemo otonashii n da te?
B: Soo rashii wa ne. Uchi de wa genki sugite komatteru rashii kedo, yoso no uchi de wa karite kita neko no yooni otonashii n datte.
A: I hear the Takahashi’s boy Masao is visiting, but he’s really quiet.
B: That’s what I hear. He’s almost hyperactive and troublesome at home, but in someone else’s home, he’s as shy and quiet as a borrowed cat.