He was simply power-hungry and knew that Maximus would be named the emperor's successor upon the emperor's death. And if that wasn't enough, he wanted Maximus family killed because he feared revenge or retaliation of any kind from Maximus young boy (sort of like wiping all traces of Maximus clean from the face of earth) Maximus was very loyal to Marcus as his general and probably would have killed Commudus for murdering his own father and this, Commudus feared.
