The Church is both Visible and Invisible, Human and Divine, because it and Jesus Christ are One, which is why the Church is One, Holy, Catholic, and Apostolic: These four marks are the marks of Christ. If the Church is both Human and Divine, and being a Divine Institution just as Jesus is a Divine Person, than it needs a Divine Head. This it has in Christ, who founded the Church on Peter. But it is also human, just as Jesus is human, so it needs a human head. But Christ only has one Head on His one Body, so it cannot have two heads. As such, the human head must represent the Divine Head. This it dose in Peter, whom Christ appointed as Pope. Christ, essentially, founded His Church on His vicar. This He did to show that He chose Peter to be His representive on Earth. It would nonsensical if He chose Peter without giving him a primacy, for how could the Church of God be founed on a human being and his faith? So He chose Peter to be His supreme pontiff, the Visible Head representing the Invisible Head, invisible to the Invisible, which is more visible than the Visible because it was He who founded the Church.
Imagine for a moment two different types of churces. One is of a church of twelve bishops, all of whom represent Christ, and none of them have a primacy. This church has twelve heads, which is unlike Christ’s Body, which only has one Head, The other is of a church of twelve bishops, all of whom represent Christ, and one of whom has a primacy. The church has one head, which is like Christ’s Body, which only has one Head. Tell me, which church is Christ’s? Which church is one with Christ?