You are Peter - and on this Rock I will build my Church and the gates of the underworld can never hold out against it. (Matthew 16:18)
In these words, Christ conveys to us two essential truths about the Church.
Firstly, it is indeed a human institution. Peter is the Rock on which the Church is built. The Body of Christ in this world is led by a man. It is a human institution, with a human face. The Church dwells in and amongst society with its cares and anxieties, its joys and its achievements. The Church celebrates the joy of the newly weds, the life of the newly born, and prays at the bedside of the sick, consoles those who grieve, guides and reconciles those who fall on the journey of life. The priests and the bishops are the shepherds of the sheep, the Holy Father the supreme shepherd of the universal Church and all of us are called to show the love of Christ to all human beings. As humans we love. We also fail. Sometimes those sheep, those shepherds, make mistakes, serve imperfectly, fail to convey God's love - but as Christ is human, so the Church lives in humanity ... it is Peter on which the Church is built.
Yet, secondly, the gates of the underworld can never hold out against the Church. Though made up of human beings, the Church is the Body of Christ, the Temple of the Spirit, the Pilgrim People of God. The Church's only purpose is to serve God and to lead all people to heaven. And God guides and protects his Church. The Papacy, the line of the successors of Peter, is the longest continuous institution in the world. Through wars, and heresy, and schism, in spite of wickedness and greed, despite opposition and persecution and ridicule, the Church persists, not only in our hearts, but as a visible institution reaching into all parts of the world, all areas of human learning and concern. The Church is holy, not because we are holy, but because God is holy.
In the words of St Paul in today's second reading:
How rich are the depths of God
how deep his wisdom and knowledge ...
To him be glory for ever! (Romans 11:33)