Its what is claimed in the Bible:
"…when you are old you will stretch out your hands, and another will dress you and take you where you do not want to go." This is interpreted by some as a reference to Peter's crucifixion. - Wikipedia!
Origen says: "Peter was crucified at Rome with his head downwards, as he himself had desired to suffer." This is why an upside down cross is generally accepted as a symbol of Peter, who would not have considered himself worthy enough to die the same way as his Savior