What is Apostolic Succession?
Just a very simple study of the most important verse supporting Peter as the presumed head of the church reveals that Jesus called him petros which Strong's defines as a piece of rock and that the church would be founded upon petra which Strong's defines as a mass of rock.
It seems all to obvious, esp. in the context, that Peter is petros, the piece of rock or smaller stone, while Jesus is petra, the mass of rock, or Chief Corner Stone. I believe it was a rebuke of Peter and all the disciples because they were constantly contending for the highest position. Plus, Peter was so impetuous that a rolling stone--a stone that could easily be tossed about with every new thing--perfectly described his character. He was always quick to blurt something out which revealed a lack of solid grounding.
Thus I believe Jesus was saying to Peter, and the others, that he (they) were small pebbles but that the church would be founded upon an immovable rock such as a corner stone--which of course is Christ and is of course what the scripture confirms in the old and new testaments.
Of course, one cannot deny the keys portion but that doesn't exactly fit into the discussion of succession.
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“Ask, and it will be given to you; seek, and you will find; knock, and it will be opened to you."