Sorry - but Jesus wasn't talking about the leadership of His Church here. He was rebuking the Apostles because they were arguing about which one of them would be considered the "greatest".
As for who would be the greatest - he must serve the others. That's why the official title of the Pope is "The servant of the servants of God".
Jesus clearly appointed Peter as the leader in Matt. 16:18-19, Luke 22:31-32 and John 21:15-19.
This is complete nonsense.
Why is it "wrong" to delegate smaller matters where there are more pressing matters?? Peter was just ONE man and could only do so much. Do YOU do everything at home and at work?? Do you run the entire company? Do you run every ministry in your church??
Then, why would you put that ridiculous expectation on Peter?
Everybody in the Body must do their share and not leave it to ONE person.
First of all - Peter was wrong when he wouldn't eat with Gentiles. Paul ALSO admitted to sinning (1 Tim. 1:15). John also told his readers that he was a sinner (1 John 1:8). - so what's your point?? That a leader of the Church cannot sin?? We're ALL sinners - including YOU.
As for your misinterpretation of Jesus calling Peter a "pebble" or "small" rock - this is a common mistake.
Jesus didn't call Peter a "pebble" - He called him "ROCK".
The Lord said to Peter: “And so I say to you, you are Peter (Petros), and upon this rock (Petra) I will build my church, and the gates of the netherworld shall not prevail against it.”
YOU say that He called him a pebble or small rock because the word "Petros" is used instead of "Petra", which means large rock. You believe that Jesus is the Rock here because he is referred to as Rock elsewhere, including, Matt. 21:42 and 1 Pet. 2:3-8. The problem with this is that Jesus didn’t speak Greek to his Apostles - he spoke Aramaic.
What Jesus actually said was: “And so I say to you, you are Kepha, and upon this rock Kepha I will build my church, and the gates of the netherworld shall not prevail against it.”
This is why St. Peter is referred to as Cephas in many of St. Paul’s letters, because Cephas is the closest Greek transliteration of the Aramaic, Kepha.
There is another problem for you here: Petra is a feminine Greek noun and would NOT be used to describe a man, so the word was translated as Petros in Scripture because it was being used in reference to a man. Jesus clearly appointed St. Peter as earthly head of the Church and Chief Apostle here in Matthew’s Gospel as well as Luke 22:31-32, where he told Peter that he prayed for him alone to strengthen the other Apostles in his absence and in John 21:15-19, where he told Peter 3 times to feed his sheep.
By the way - Abraham is ALSO referred to as the "Rock" (Kepha) (Isaiah 51:1-2).