What the 12 bound on earth was bound in heaven and what was loosed on earth was loosed in heaven. They were to preach the gospel to every creature. But lookie here, in Galatians. "When James, Cephas (Peter), and John, who seemed to be pillars, PERCEIVED THE GRACE that was given unto me, they gave to me and Barnabas the right hand of fellowship; that WE SHOULD GO TO THE HEATHEN, and THEY UNTO THE CIRCUMCISION."
They loosed themselves from their commission to take the gospel to every nation, and gave Paul the right hand of fellowhsip to take HIS GOSPEL OF THE GRACE OF GOD TO THE GENTILES. Peter and the 11 confined their ministry to the Jews.
Now if you believe you are a Jew, then maybe you would have an argument regarding Peter's "successors". But Israel has been blinded and set aside until the fulness of the Gentiles be brought in. So it does you absolutely no good to claim to be Israel today. The Body of Christ is made up of neither Jew nor Gentile, male nor female, etc. So, the question is, WHAT "successors" to Peter? What exactly would they "succeed" him WITH? The only question remaining should be "why did Peter and the 11 loose themselves from the commission given to them by Christ? And make no mistake, it was not an accident. It was not laziness, or an inability to fulfill their commission. It was COMPLETELY IN LINE with God's Plan. And they perceived that when Paul and Barnabas told them "that gospel they preach unto the heathen".
Paul goes on in Corinthians to preach that he was the least of the Apostles and unworthy to be one because he persecuted the Church of Christ.