To begin I just want to say that there are books written on this one question going over the theology in depth and covering a lot more of the reasons behind it. Below you will read the three reasons that over the past three years have had the most impact with the students in the 3 to 5 minutes that I have their attention. This answer is just of the tip of the iceberg to help them begin to understand this teaching of our faith. If you have any questions regarding this question, please comment and I will help lead you to some great resources.
The first is that the priest, especially when they are on the altar at Mass, are a representative of Christ. During the prayer of Consecration the priest says “This is MY body given up for you” and “This is MY blood poured out for you”. He does not say “this is Jesus body” and “this is Jesus blood”, he is in that moment what we call In persona Christi which is Latin for in the person of Christ. The priest is a physical representation of Christ for us and as history tells us Jesus was a man. Thus a priest is a man.
The second reason and one that sticks most for me personally is that the best female candidate to be a priest would have been Mary. Mary was born like Jesus without sin, she was there for all of Jesus miracles, she was there when he died on the cross and was present at Pentecost. Mary is our example of a perfect disciple and the MOTHER of God Himself, if she was not chosen to be a priest than no other woman created would ever be worthy to have that ministry.
The third is simple: Jesus chose men, He had other women followers but He chose 12 men to take His place. What gives us the authority to change what God Himself put in place? Now some people might say that Jesus chose men because of the time that Jesus lived, women were not treated the same as men. However we need to look no further than the Bible to see that Jesus did not care about that. Jesus broke through the cultural barriers when it came to women: look at the Samaritan woman at the well- culturally men were not allowed to speak to women outside their own family-Did that stop Jesus… No. Look at the story of Martha and Mary- women were not being educated- yet Jesus taught Martha and even rebuked Mary for not stopping to learn and listen. Who was the first person to see what is known as the greatest event in human history- Jesus’ Resurrection… none other than Mary Magdalene- a WOMAN! Those are just a few stories, there are many more stories in the Gospels that show Jesus did not care about what the law or culture said about women and men but rather regarded them with the same respect as both being created in God’s image and likeness. God’s plan was to have men follow in Christ’s example in the priesthood and women to take on different roles, each complimenting their unique gifts.