Peter was the first Pope, upon whom Christ built His Church. Every Pope since has been the direct successor of Peter himself. As the Vicar of Christ on earth and the head of the Church He established, the Pope speaks with authority on matters of faith and morals. Such as the Queenship of Mary and Immaculate Conception
"There are also many other things that Jesus did, but if these were to be described individually, I do not think the whole world would contain the books that would be written." … John 21:25
No. Peter had an important role to play, as did Mary. Peter was not supreme - Paul said he was in now way inferior to the other Apostles, and Peter was "afraid" of men sent by James. Jesus Himself told the Apostles flat out when they argued over who was the greatest that they were missing the point - God is the greatest, but we are all to be servants.
He opened the doors to the Jews at Pentecost, and to the Gentiles a little later. The Church is built on Peter's confession, "You are the Christ, the Son of the living God."
The pride and arrogance that led to the Bishop of Rome claiming authority over the other bishops is what caused the downfall of the Catholic Church. When the bishop of Rome branded people as heretics for celebrating Easter at Passover rather than the day he picked, he demonstrated a total lack of understanding of Christ.
It has only become worse with time.
Heaven has a King, and there is no 'Mrs. God' sitting beside Him. John Paul II wrote "In this divine marriage with humanity Mary answers the angel's announcement with the love of a spouse who is able to respond and to adjust to the divine choice in a perfect way. For this reason, especially since St Francis of Assisi's time, the Church calls her "the spouse of the Holy Spirit". Only this perfect marital love, deeply rooted in her total virginal self-gift to God, could have brought it about that Mary became the "Mother of God" in a conscious and worthy fashion, through the mystery of the Incarnation.
In the Encyclical Redemptoris Mater I wrote: "The Holy Spirit had already come down upon her, and she became his faithful spouse at the Annunciation, welcoming the Word of the true God, offering 'the full submission of intellect and will ... and freely assenting to the truth revealed by him'..."
Those are words of blasphemy, not "The Vicar of Christ". I've read all the verses where Jesus addresses his mother in public. He doesn't even call her "Mother"! He addresses her as "Woman". Not Queen. Not Mrs God. Not Mother.
Woman. Even in his final agony, "26 When Jesus saw his mother and the disciple whom he loved standing nearby, he said to his mother, "Woman, behold, your son!" 27Then he said to the disciple, "Behold, your mother!"
Think about it. There is more scriptural warrant for calling Mary the "Mother of John" than there is for calling her "Queen of Heaven".