The tension in the rope on one side of the pulley is trying to rotate the pulley in one direction, and the tension on the other side is trying to rotate the pulley in the opposite direction. If the pulley is rotating at a constant speed, then the net torque on the pulley has to be zero, which means that the difference between the torques from the two ropes has to exactly cancel the torque from friction. The frictional torque is non-zero, so the difference in the tension of the ropes has to be non-zero, which means that it can't be the same in both ropes.