Why did Michael have Freddo killed?  He betrayed him.  End of story.
As portrayed in these (and other similarly styled) films, the Mafia
is a larger and more demanding family than the traditional human family.
And it requires a deeper and a stronger loyalty.  Freddo betrayed both.
Sick and broken, perhaps, but guilty of something that could not be
forgiven, he had to be disposed of.  Without unfailing loyalty, there is
no security in the family.  Part III shows us well how that pans out.
                                               Shari L. Rosenblum