The wire attached to the negative terminal of the battery didn’t turn green because the reaction that takes place there cannot form copper hydroxycarbonate. In order to form that compound, you must have oxygen, and oxygen is formed only at the wire connected to the positive side of the battery. On the wire connected to the negative side of the battery, hydrogen is formed.

Without oxygen, no copper hydroxycarbonate can form, so the battery attached to the negative terminal cannot turn green.