All Thirteen looked identical, - be it their Garments, Hairstyle, Facial grooming, Footwear, Physical Structure, Body Language etc.
For an outsider it was definitely difficult to identify the Master, until he spoke.
To ensure they did not arrest the wrong individual and send to condemnation, they had to have one among the Twelve identify the Master.
Rather than denounce the betrayer, we have to accept this as God's plan to avenge the Fall of Man.