But why does Michael have Al Neri dig up dirt on Tom and then Michael agressively asks Tom (during their meeting when he mentions Tom's mistress) if he is leaving the family business or going to go along with the things that he has to do? Tom asks hom why he hurts him like that? Is it simply because of Michael still holding him responsible for Sonny's death or something else?
I think there's more to it. Michael is a master manipulator.
Earlier, he uses Tom's desire to be viewed as a real brother to manipulate Tom. Later, when Tom begins to get out of line, he puts Tom on the defensive by being hurtful.
In both cases, he achieves his goal of getting Tom's loyalty and quiet submission.