Christians think of justice in terms of being the defendant in a court. As a result, we are terrified of the prospect because no Christian is completely blameless. The Psalm writers thought of themselves as plaintiffs in the court demanding justice for themselves. Most of the time, the court of justice would be a civil court, not a criminal court.
“Indeed what is called ‘sensitiveness’ is the most powerful engine of domestic tyranny, sometimes a lifelong tyranny. How we should dal with it in others I am not sure; but we should be merciless to its first appearances in ourselves.”
There is a fine line between being right and being righteous. The Psalmists cross that line occasionally. Jesus was clear about people who thought they were righteous—there is nobody who makes that standard.