The real question is why should there be a ministerial priesthood in addition to the universal priesthood all Christians share. To understand this, let's back up for a second. Human society requires a division of labor. Within civilization there is no such things a true jack of all trades. The mountain men of the 19th century may have been rugged, but they also had amazingly short lifespans, no more than a few years once they left civilization.
Man is a social being.
There is a good reason for this. The holy things are the most important things there are, meaning that they of all things require a specialist to minister them. The chief act of corporate worship for a priest is the offering of sacrifices to God on behalf of the people. If God required specialists to perform even the dead animal sacrifices, how much more will he require specialists to play a role in the living Christ's offering of himself to his Father. This is all the more apparent when one considers the Real Presence of Christ in the Eucharist.