A wonderful talk given by Hyrum W. Smith in 1988 at Rick’s College (now BYU-Idaho), “Why 1820?”
From 1975 Ensign by Richard Lloyd Anderson: Simon Peter
A few paragraphs below:
“Was Peter impulsive, pious, or vacillating? Was he the first pope?
These questions reflect distorted opinions of the personality and life of Christ’s chief apostle. The authentic Peter towers in the New Testament, where more information is found on this apostle than any other except Paul.
None of the first disciples is mentioned as frequently in the gospels and the Acts; Peter’s recorded speeches, letters, and deeds exceed what remains from any other original apostle.”
From Elder McConkie in 1981:
Key section of Elder McConkie’s talk:
“Blessed art thou, Simon Bar-jona,” Jesus says, “for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.” (Matt. 16:17.)
Then again Jesus alludes to the difference in paternal ancestry between him and Peter and continues his words of blessing and doctrine by saying: “And upon this rock”—the rock of revelation—“I will build my church; and the gates of hell shall not prevail against it.” (Matt. 16:18.)
And how could it be otherwise? There is no other foundation upon which the Lord could build his Church and kingdom. The things of God are known only by the power of his Spirit.
God stands revealed or he remains forever unknown. No man can know that Jesus is the Lord but by the Holy Ghost.
From the LDS Student Manual on Matthew 16-18:
Matthew 16:18. Revelation Is the Rock upon Which the Church Is Built
As the Savior taught Peter about revelation, He used a wordplay on Peter’s name, declaring to Simon, “Thou art Peter [Petros], and upon this rock [petra] I will build my church” (Matthew 16:18).
The Greek word petros means an isolated small rock or stone. The Greek word petra can also mean “a stone,” but in addition it can refer to stony soil, bedrock, or a large mass of rock.
From these words we learn that it was not upon Peter as a man that the Church would be built, but upon the bedrock of revelation.
To read about the significance of Peter’s name being changed from Cephas, see the commentary for John 1:42.
President Howard W. Hunter (1907–95) taught: “‘And upon this rock I will build my church.’ Upon what rock? Peter? Upon a man?
No, not upon a man, upon the rock of revelation, the thing which they were talking about.
He had just said, ‘… flesh and blood hath not revealed it unto thee, but my Father which is in heaven.’ This revelation that Jesus is the Christ is the foundation upon which he would build his Church” (in Conference Report, Oct. 1965, 112; see also Teachings of Presidents of the Church: Joseph Smith , 195)
This talk discusses what this part of the verse means. A few paragraphs below:
“The Greek word used to denote church in Matthew 16:18 is ecclesia, which literally means a “calling out” and originally referred to a civil assembly. Thus Jesus’ use of the phrase “my church” referred to an assembly “called” by him.
In the present dispensation, the Lord used church in this same sense. He revealed to the Prophet Joseph Smith that “whosoever repenteth and cometh unto me, the same is my church. …
“Behold, whosoever is of my church, and endureth of my church to the end, him will I establish upon my rock, and the gates of hell shall not prevail against them.” (D&C 10:67, 69.)
In these instances the “church” is not so much an institution as it is a group of individuals who repent, come unto Christ through the ordinances of the gospel, and endure in faith to the end. Upon them the adversary has no claim.”
We all must be personally built upon the rock. Read this 1992 Ensign talk: Built Upon the Rock.