Jesus is our high priest, not because he comes from the right family. He is our high priest because he defeated death - he was indestructible! (Hebrews 7:16)
Not all people have a concept of what a priest does - (or if they do it is stained and corrupted by a connection with children being abused). But I think everyone wants someone on their side, someone who will stand up for them when they have to plead their case or tell their story.
The writer of Hebrews calls the Jewish priests, or their interceding work, weak and useless, because it cannot change lives. Jesus brings a better hope - he is not weak or useless, he is indestructible and perfect forever (Hebrews 7:28)
I see so many people who need that. And I need that.