The virtues you list would be ideal to be found in a priest but not only in a priest but in each of us, especially those called to be counsellors. A priest, however is not primarily a counsellor, he is someone who primarily offers. sacrifice.
A Catholic priest at Mass offers the Sacrifice of Christ upon the Cross in an unbloody, Sacramental manner throughout time and he does this at Christ’s bidding in the place of Christ. 
God willed that Christ His anointed one be born a man which surely must have some significance in the scheme of things. Christ uniquely became both priest, High Priest and  Victim when He offered Himself to the Father on the Cross for the sins of the world. The apostles and their successors have preserved this essential maleness, this charism of Christ’s High Priesthood in the priesthood of Christ’s Church.
Would that people accept this today as they have done for over 2 millennia up until today. Why, asks the psalmist, “.. do people imagine a vain thing.”(Psalm 2).