The icon is seen by too many Catholics as the institution to be relied upon. The Church, the ekklesia, is not an institution, it is The Body of Christ. Neither Paul nor Peter is Christ’s head, for God Is The Head.
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To help us understand, we can look at an Old testament type prefiguring the Apostles in their role as “pillars”. In the Temple of Solomon there were two prominent bronze pillars. These pillars are given names in Scripture. The first pillar is Jachin, which means “the Lord will establish” . This notion of establishing can be linked to our Lord telling Peter: “You are Peter and on this stone I will build my church.” The second pillar is called Boaz, and here we have an even more surprising relationship, because although the word Boaz has an obscure etymology, it refers to the ancestor of David known mostly for marrying Ruth, a gentile woman who converted. Boaz therefore strongly prefigures Paul as the “apostle to the gentiles”. Most importantly, just as with Peter and Paul, we can see in the two pillars of the first Temple this primordial movement towards and away from the center, analogous to the movement of the nous.
http://www.orthodoxartsjournal.org/st-peter-on-the-right-st-paul-on-the-left/