The controversy surrounding the ordination of women to the priesthood could be easily resolved by accepting what the Bible says on the subject.
Let's begin answering the question by way of a brief historical overview.
The priesthood did not begin with the coming of the Christian faith. It has a long and distinguished pedigree spanning most of the Old Testament. We first meet Israel's priests shortly after Israel left Egypt on their way to the Promised Land. From among the twelve tribes that composed the nation of Israel, God chose the tribe of Levi as the tribe from which the priests would be chosen. Priesthood was therefore based exclusively on ancestry. The priest functioned on behalf of the people and was attired in special robes in the execution of his duties. (Exodus 27-29; Leviticus 6:12; 10:11)
A Royal Priesthood
It was never God's intention that this type of priesthood should last forever. With the coming of Jesus, a priesthood was established that would include all God's people and not just the select few as in the Old Testament. The priests of Israel offered animal sacrifices for the sins of the people. These sacrifices never secured remission of sins; they served to point to the day when God would provide the perfect sacrifice whose death would pay in full the penalty for our sin. Through his sacrificial death upon the cross, Jesus secured the remission of our sins and introduced a new priesthood composed of all people - irrespective of race and gender - who are "born again of water and the Spirit." (John 3:1-8)
Offering Spiritual Sacrifices
Writing to his Christian brothers and sisters, the Apostle Peter says, "But you are a chosen people, a royal priesthood, a holy nation, a people belonging to God, that you may declare the praises of him who called you out of darkness into his wonderful light." (1 Peter 2:9) And the Apostle John tells his fellow Christians, men and women, that Jesus "has made us to be a kingdom and priests to serve his God and Father – to him be glory for ever and ever! Amen." (Revelation 1:6)
The Bible is clear: every Christian is a priest and a member of "the royal priesthood", "a holy priesthood" and is engaged in "offering spiritual sacrifices acceptable to God through Jesus Christ." (1 Peter 2:5,9)