Well, first of all, it isn't that he can't play at this position at all, but he wouldn't be as good as some people think he would be. Of course, he could play there once or twice if all our Holding Midfielders are out. The main reason for which some people want Luiz to play as a Midfielder, it is because he does make his well-known runs forward. But the truth is, if he is played as a Midfielder, he won't be able to make these runs. If he is capable of making such runs, this is because he is a defender, and when you are a defender, you never have an opponent to chase you down. Indeed, the other team's players are already busy with your fellows playing in midfield and in attack. Thereby, Luiz is able to reach the opponent's box without facing any resistance, and he has a clear way. So, if he was playing as a defensive midfielder, he couldn't do that, because he would permanently have a player on his back to press him. Furthermore, I don't know if you have noticed, he always starts to run from his own 30 yards, he thus reaches the opposition with a fair amount of speed... If he was playing in midfield, he obviously wouldn't be able to make that. And what is very interesting with him playing in defense, is that he can help out the midfield to break the opposition's defense by outnumbering their midfield/defense. Considering the actual context, i.e. our midfield's inability to create things, this help from our very own SideShow Bob is welcomed. Once again, he wouldn't have this effect if he was playing in midfield. Finally, a Defensive Midfielder has to sit back to help out with the defensive duties. Makelele was doing this, Busquest does this, as Romeu and Mikel. I am not really sure he has the discipline to do this. You could argue if he hasn't the discipline to be a DM, he neither can be a CB. But, when he leaves out his position, there's Ivanovic who slides to the axis, and Mikel/Romeu staying near Terry. Well, I hope to have been understandable, lol.