I always thought David Luiz plays like he is the main character in his own imaginal movie.
Always this overemotional additude, always trying to play the Hero. Television doesnt highlights those blunders he make, the masses think that if a player is not involved in a situation, then he cant be blamed for it, but thats just where the mistakes start for David Luiz.
Whenever PSG is moving back in a defensive formation and the opponent attacks on the wings, David Luiz often leaves his position for complete unnecessary reasons, probably because he thinks that the fullbacks and CDMs hes playing with are not David Luiz and therefor cant get the job done. Then he leaves holes open and the opponent scores. He's completely unable to communicate or trust his teammates and then he endangers his backline.
Hes always running in the direction he is looking at and he is always looking at the ball, like a playful dog. He completely ignores everything around him and he lacks the courage to stay passive when he has to. He would be a great CDM in pressing systems and his quality on the ball is outstadning, but if we'd just reduce it to the position he is used at, if we'd just reduce it to the most important job he has to do (defending) then he would hardly be a famous footballer who is in matches on TV all over the world.