I can't insert a new edge loop I can't select all the faces even if they are on the same plane. I don't understand. There are no double edges, vertices or faces. I want to insert a new edge loop (Ctrl+R) but can't create one all around.
I realized there was a double edge on one of vertical edges. So there was a disconnection between the edges. I used W > Remove Doubles operator however it didn't solve the problem so I should have deleted those vertices manually.