Christ came as the new "Adam" in the sense that He began a new creation in humanity - a new, redeemed and holy humanity. He is also the "last" Adam, as God has planned only two "generations" of men- the first, from Adam, which would fall into sin; and the second and last, who would rise in Christ.
1Cor 15:45 Thus it is written, "The first man Adam became a living being"; the last Adam became a life-giving spirit.
The priests of the Church have the ordained authority to celebrate the sacrifice of the Mass, in which the priest repeats the words of Jesus, by His command (when He said, "
Do this in remembrance of Me"), "This is
My Body", and "This is
My Blood..." A woman cannot obey that command; she cannot say "This is
My Body" in the person of Christ. Thus the priest stands "in persona christi capitas" when he celebrates Holy Mass. Thus the Church says, simply, that she does not have the authority - in herself - to give this authority to woman. She - the Church - only has the command to obey it as given.
Thus Christ is the 2nd and last Adam. Adam was the progenitor by flesh of the first generation of men; Christ the progenitor by Spirit of the second and last generation of men - those born again by the Spirit into His death and resurrection.
And priests stand in His place. Mary, by the way, was recognized early in Church history as - parallel to Christ the new Adam - as Mary the new Eve: the new mother of the new humanity in Christ. This role of Mary in God's work of the new creation in Christ is thus foundational to the Marian devotion in the Church.