A priest has a distinct role in scripture of standing in the gap between God and man. He was the one to make sacrifices on behalf of the people. But now we have a perfect and great high priest who was our sacrifice. Similarly, fathers can walk in the way of Jesus as they lead and sacrifice for their families.
"Therefore he had to be made like his brothers in every respect, so that he might become a merciful and faithful high priest in the service of God, to make propitiation for the sins of the people." Hebrews 2:17