Matthew 27:24
24 When Pilate saw that he could prevail nothing, but that rather a tumult was made, he took water, and washed his hands before the multitude, saying, I am innocent of the blood of this just person: see ye to it.
Pilate washed his hands to show he had nothing to do with the crucifixion of Christ, but in reality he did. In reality he was a sinner who needed to be saved so his sin was the reason for the crucifixion. We are all responsible for his death because we were born into sin. The one thing that sets us apart from sinners is the fact we accept him and his sacrifice to wash us clean. So when you look at the sinner and think Christ died for that scum, remember, it was also your sins that he hung on the cross for as well.