1) The Hebrew Christians thought they had lost their means of intercession through the old priestly system, but Jesus provides them a more supreme mediator.
2) As their heavenly High Priest, Jesus offers the perfect sacrifice once for all time to set people's consciences completely at ease before God.
3) Unlike earthly high priests who had to offer sacrifices for their own sins, Jesus is sinless and the perfect high priest who mediates on behalf of others.