Did you miss this? Simon, behold satan has demanded to sift you like wheat, but I have prayed that your own faith may not fail; and once you have turned back, you must strengthen your brothers.
It is quite clear that Peter is singled out to play the role of a leader and unifier among the Apostles. Therefore, he is not merely one Apostle among others. Rather, he is also responsible for the welfare of all.
Jesus calls Peter "blessed" (makarios in Greek). This word always denotes the blessedness of the person whose relationship to God is correct and holy. Read Mt. 5:1-11; Rom. 4:7-8; Lk. 1:45. There is another word for "blessed" (eulogetos in Greek) which is used only of God and means "Praise". For example, Lk. 1:68
Blessed (
makarios) art thou used in relation to
Peter is in
Mat 16:17 and in
Luke 10:23 in elation to
all His disciples 
In John 20:29 regarding
~those~ who have not seen (
as they have) and in
1Peter 4:14 from Peters words
to others regarding
the Spirit of glory resting on one. Thats why they are blessed. That shows nothing that shows your point.
The majority of the time the other word "
blessed" (
eulogetos) is used is in relation to the "
bread". In Mat 16:26 , Mark 14:22, Luke 24:30 Showing the same in 1Cr 10:16 The cup of
blessing (
eulogetos) which
we bless (
eulogeō), is it not the communion of the blood of Christ? The
bread (
artos)which we break, is it not the communion of the body of Christ?In
Luke 1:42 the angel uses
blessed (
eulogetos) regarding
Mary herself

and the other
Blessed (
makarios) "following that" in
Luke 1:45. So both are shown. In other places its used by the people who say "
blessed" is he that comes in the name of the Lord
Luke 13:35.
But in relation to
the disciples were called
Blessed (
makarios) in Luke 10:23 Trento.
Paul says WHO is Cephas? Paul did not say, "Peter is the head" or beyond reproof. It was Paul was the one who spoke more of the unifying factor Peter withdrew himself from. Peter is clearly not beyond correction or erring.
They dissamsembled in Peter (good lesson in history). It was Paul who had the courage to speak up and saved him from his own demise (and those who followed him). Ofcourse Peter erred. If we follow any man not acting in accordance with the truth those who follow them will fall right on top of them. Only insofar as one follows Christ are we.
Peter (Mr head?) has no problem pointing to Paul (He could at least see beyond himself) and could reccognize others too walk in the truth (sometimes a little better then he did)
In light of your explanation regarding Peters ~right relationship~ with the Lord over the word ~makarios~ (wherein the Lord calls all his disciples such) and not just Peter... Why wouldnt you chose rather to compare Peter with the disciple who the Lord loved? Doesnt prove your point?

That (to me) would speak of one having a greater relationship with Him
Afterall it was Peter who asked about the disciple Jesus loved...and The Lord seemed to say "its none of your business" (in so few of words).
I just dont ever get ones "reasonings" or what you might use to reason a thing that appears nothing out of the ordinary.
Peace
Fireinfolding