Merry Christmas to all!!

Michael was mostly "obligated" to order Frdo's death,in a way that during the whole Part II his was almost obsessed with the idea of being betrayed.

So he wanted to let people around him realize that not even his own brother can be forgiven.

Remember Frankie 5 Angels: He didn't have to order his suicide,Frankie was a good guy.
Remember Michael's hints to Tom Hagen...

During the whole movie he becomes more and more cruel and ruthless.

And that's what he pays for in Part III...