Again the Greek word for Peter's name is not the same as the rock Jesus was talking about.
HTML Bible Index - King James Version - Strongs Concordance - Frames Version
Go to this site, in the left column scroll down to Matthew in blue and click on the #16 in blue to pull up that chapter. Then scroll down on the right to those verses where the Greek words in blue are mirroring the verses in English.
Then click on PetroV for the name of Peter and then click on petra for the rock Jesus is talking about in verse 18.
PetroV is "apparently a primary word;
a (piece of) rock (larger than 3037); as a name, Petrus, an apostle:-
-Peter, rock. Compare KhfaV - Kephas 2786.
Kephas or Cephas is stone; piece of rock.
Petra is "feminine of the same as PetroV - Petros
4074;
a (mass of) rock (literally or figuratively):--rock.
So not the same Greek word nor the exact same meaning for why Peter's name is regarded as Cephas or stone. If it was exactly the same meaning, then "petra" would be unnecessary, but it was necessary because the difference is size.
Same keys given to His disciples and so you are forgetting that there were other disciples in that room when you applied Jesus's words only to Peter himself.
Matthew 16:19 And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven. 20 Then charged he his disciples that they should tell no man that he was Jesus the Christ.
These keys to binding and loosing is given to every believer abiding in Him in correcting others, even those considered the little ones that go astray.
Matthew 18:14 Even so it is not the will of your Father which is in heaven, that one of these little ones should perish.15 Moreover if thy brother shall trespass against thee, go and tell him his fault between thee and him alone: if he shall hear thee, thou hast gained thy brother.16 But if he will not hear thee, then take with thee one or two more, that in the mouth of two or three witnesses every word may be established.17 And if he shall neglect to hear them, tell it unto the church: but if he neglect to hear the church, let him be unto thee as an heathen man and a publican.
18 Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven. 19 Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven.
So Peter is not so exclusive as you had been led to believe.
As important as that line of succession is per the CC, we do not see that as being taught as such in the N.T. That was just a con line to keep the authority of ruling over the churches from Rome.