Yes they should on 7 grounds:
1)By being Baptized we share in the same common bond to Christ. As Catholics we are called to the priesthood of all believers.
2)One big factor is the Last Supper. The truth about the Eucharist is that all are called to the table, both men and women receive Communion.
3)The longstanding bias against women is starting to be proved wrong. Women can and do become doctors, lawyers, theologians, etc. Many own their own company and are just as successful as men.
4)Women have always played a role in the Church. A nun is simply a priest without the ordination, at the same time both nuns and priests are called to serve. Why not extend those benefits to women?
5)The Church honors Mary the Mother of our Lord. Many other women like Mary Magdalene have proved to be some of the most solid desciples, and Jesus verified this. One way was by appearing to Mary Magdalene after rising from the Dead.
6)With all this priest shortage scares going around, allowing a small number of women would relieve some of the strain guaranteed. Its like having a good resource waiting to be tapped into and yet going through life missing the opportunity to use it to its full potential.
7)It all comes down to a love for God. Should someone ignore the calling of God? Most of this stuff against women priest is not that there shouldnt be, but that women are unable. Does this bother anyone? In otherwords it is not condemned as an evil thing, but as something that someone doesnt want because they see women as inferrior. The fact that so many women have become Saints, from StMary Magdalene to St Catherene, to St Terese of Lisieux, to St Faustina, hopefully a St Teresa of Calcutta. Does God love them any less? Does He seclude them from doing His will? Those women are Saints, proclaimed by the Bride of Christ! Notice the word “Bride”.
As Christians, and most of all as Catholics let us rise and show the world.