There is an interesting knot in Acts 4: the story concerns authority. The rulers are exercising authority over Peter and John. They want to know what authority gave Peter and John the power to heal someone. Peter takes authority by speaking. They demand obedience and Peter asks whether he should obey God or man. Peter addresses the men as “Rules of the people and elders”.
This then works out in a very ironic manner. Peter says the authority was “Jesus Christ of Nazareth, whom you crucified.” The ultimate exercise of authority by the State is death. But the State has no authority over Jesus (which Peter notes when asks whether they should obey God or man).
This is an almost comic taunt: Just a bit ago, you killed someone. That man you killed is not only not dead, he is actually making lame men well.
In Acts 3, in the public sermon, Peter tells the people that they had rejected Jesus, but “you acted in ignorance, as did your rulers”. But when Peter makes the charge in Acts 4, he removes the reference to ignorance.
When Peter and John return to the other believers, they pray, first praising God his sovereignty over the death of Jesus. (They quote Psalm 2 and say, “whatever you hand and plan had predestined to take place”).
When they petition God, they do no ask God to exercise his authority to make the persecution stop, but rather to give them the courage to continue witnessing to Jesus.
The exercise of authority in the story is thus working on two levels: The government seeks to exercise authority over the body by killing and beating. The disciples realize there is a greater degree of authority: Jesus has complete authority over the body. He cannot die. He can restore the body from injury.
Obeying God rather than man, is because God not only has a greater claim, God has greater authority.