One of the graces of Baptism is to share in the priesthood of Christ. (1268). We then share in His prophetic and royal mission which is the common priesthood of all believers. That does not include His ministerial priesthood which is conferred by the Sacrament of Holy Orders. That office is in the strict sense of the term a service. It is entirely related to Christ and to men.

  The sacrament of Holy Orders communicates a sacred power which is none other than that of Christ. The ministerial priesthood has the task not only of representing Christ—the Head of the Church—before the assembly of the faithful but also acting in the name of the wholr Church when presenting to God the prayer of the Church and above all when offering the Eucharistic sacrifice.

  Note that in the name of the whole Church  does not mean that priests are the delegates of the community. The prayer and offering of the Church are inseparable from the prayer and offering of Christ, her head; it is always the case that Christ worships in and through his Church. The whole Church, the Body of Christ, prays and offers itself through him, with him, in him, in the unity of the Holy Spirit, to God the Father. It is because the ministerial priesthood represents Christ that it can represent the Church.

  This explanation follows almost exactly the presentation in the Catechism because of possible misunderstandings that have led to some advocating  the ordination of women to the ministerial priesthood. The Magisterium of the Church does not find any evidence of that possibility in the Deposit of Faith which was completed at the death of the last Apostle.