Was the actor playing Tom demanding too much money?Fredo put the entire family at risk in order to potentially gain something. Not just "something for me" but...Fredo likely also thought getting rid of Michael would lead to him becoming the head of the family. Michael had to do it. Imagine Michael's thought process....he had to be thinking Fredo might one day endanger his son, the heir of the family.
BTW this reminds me of when Michael was antagonizing Tom towards the end of Godfather II. Michael had to re-assert his dominance over the family. Tom had been running things while Michael was away...now he had to make everyone realize he was back and the HNIC. What a shame that they couldn't get the original Godfather III idea filmed, which involved Michael and Tom battling for control of the family.