Apple and Turnbull's posts raise a point that I find very interesting. That is whether Fredo actually had a larger role in the business before Vito was shot and that his actions proved he wasn't up to the task.
To sum up Michael, he is fiercely loyal to his family and will do anything, however wrong (putting it loosely), to protect the Corleone name.
I sort of feel that Michael feels like he has the weight of the world on his shoulders and in a sense he does. He felt that he had so save the family, he felt that he had to kill Solozzo and McCluskey.