In his mind, if he showed any mercy or forgiveness to anyone who "injured " him--even his own brother-- (as he put it to Cardinal Lamberto in III), it would be viewed as a sign of "weakness" by enemies and friends alike--and would endanger his life. "
This all runs back into the earliest conception of the movies, and into the novel. Michael is a rationalist - the mathematics professor - and the inheritor of what Coppola called Vito's "intelligence, cunning and coldness." He just does calculations in his head, and dishes out what's deserved, no matter who's on the other end of it.
In the novel, Kay reflects that she loves that Michael is "always fair." Fairness can have a dark side - when crossed, a fair person can proceed completely without conscience in settling the score. That's Michael.
