In Zero-Knowledge Proof where we take the analogy of Peggy (Prover) and Victor (Verifier):
In this story, Peggy has uncovered the secret word used to open a magic door in a cave. The cave is shaped like a circle, with the entrance on one side and the magic door blocking the opposite side. Victor says he'll pay her for the secret, but not until he's sure that she really knows it. Peggy says she'll tell him the secret, but not until she receives the money. They devise a scheme by which Peggy can prove that she knows the word without telling it to Victor.
First, Victor waits outside the cave as Peggy goes in. They label the left and right paths from the entrance A and B. Peggy randomly takes either path A or B. Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random. Providing she really does know the magic word, this is easy: she opens the door, if necessary, and returns along the desired path. Note that Victor does not know which path she has gone down.
However, suppose she did not know the word. Then, she would only be able to return by the named path if Victor were to give the name of the same path that she had entered by. Since Victor would choose A or B at random, he would have a 50% chance of guessing correctly. If they were to repeat this trick many times, say 20 times in a row, her chance of successfully anticipating all of Victor's requests would become vanishingly small. Thus, if Peggy reliably appears at the exit Victor names, he can conclude that she is very likely to know the secret word.
The following method of verification is convincing enough for me:
Victor goes through both corridors A and B and assures himself that there is no way one could go to the other end.(Since Victor has no knowledge of secret, he is convinced himself this is true).
He could go to entrance of corridor A, ask Peggy to go through entrance B and come from the end of A. (Peggy does, and comes out of end of A)
Victor would also proceed the other way where he stands at entrance of B and ask Peggy to come though end of B after going through A.
If Peggy could do both 2 and 3, Victor is convinced that Peggy knows the secret.
I feel that this method is wrong and wonder why. So, why would classical method be preferred over this? What are the weaknesses of this method?