You have to understand that it is impossible to separate the family from the Family. After all, Fredo was responsible for gunmen shooting up Michael's home. It doesn't matter if he knew it was going to be a hit or not. He set up Michael for some sort of harm, because he had to know that whatever dealings he had with Roth and Ola (and they had to be somewhat extensive if he knew who Roth's man was at the senate hearings), he had to realize they weren't coming to Michael's house to deliver oranges.

Fredo put the family and the Family in harm's way. When he revealed his bitterness and envy, he also revealed the fact that, if he wasn't eliminated, he could do so again.

As for my "turning into Michael Corleone", why Thank You, Cristina. Rarely has someone said a nicer thing about me.