The desire for revenge in a complex form is what drives Matt. He feels an unspeakable loss in the wake of his son's murder. He combs through the emotional wreckage that represents his life, constantly plagued by what else he could have done to keep his child safe. He examines and reexamines his actions and the thoughts continue to come back to his unresolvable condition of grief and remorse. In order to alleviate his pain and assert his role as protectorate for his family, Matt channels his energy in killing Richard.
It is a desire for vengeance that propels Matt, but it is also layered in the belief that killing Richard will represent Matt protecting his family from an existential threat. Matt becomes consumed with this as a way for his own pain and guilt to be lessened. It is this desire that propels Matt forward. Matt plans and conspires with his friend, Willis, as to what they will do and how it will be done. Matt's meticulous planning and focus on the deed as something more than a mere whim reflects how his desire to kill Richard is what keeps him moving forward, propeling him into a realm where he believes emotional hurt can be remedied through the use of violence.