Those leaders listening to Peter are the “heavyweights” in top positions of authority in the Temple and in the Jewish community, especially the Sadducees. A cripple has just been healed by the power of the name of Jesus, through the ministry of Peter and John. What really bugs the Sadducees is related to their non-belief in the resurrection of the body. So, the healing of the man crippled from birth is not really he point of argument at all. Rather, it is the fact that Peter and the other apostles are preaching that Jesus rose from the dead. Everything else gets lost in the stubbornness and hard heartedness of the Sadducees about resurrection.
When Peter calls for the conversion of his listeners to believe in the resurrection, pointing to the salvation which is only available through Jesus Christ, it brings immediate opposition from those with closed minds and closed hearts. Still, the leaders are bewildered by the eloquence of this simple fisherman. This was a surprise to them for Simon Peter had none of the education in the Torah to which the other rabbis and priests and scribes had been exposed. The reality of the crippled, but now healed man, standing in front of the gathered community leaders, spoke volumes in testimony about the “name” of Jesus and his power. So all that these leaders could do was to threaten the apostles and warn them against continuing their preaching about the resurrection.
God always seems to prefer to use the “ordinary” things to demonstrate his mighty power – in this case an “ordinary” fisherman. He uses the humble to confound the wise. In any event, the message is clear: when a Christian steps out in faith to proclaim the Good News, it can be expected that a possible consequence will be instant resistance and antagonism from the established culture.
The very name “Jesus” specifies that the very name of God is present in the person of his Son – it is that divine name that alone brings salvation. Without faith in Jesus no one will attain eternal life.