Why could the religious council say nothing against Peter and John after the healing?
The council could say nothing because the healed man was standing with them as visible proof of a genuine miracle. They recognized these unlearned men had been with Jesus, and they could not deny the notable miracle done openly before all Jerusalem.
Les explains that the magistrates and religious leaders saw Peter and John were unlearned and ignorant men, not taught by the rabbis or trained in a seminary. Their only preparation had been the presence of Christ for three years, yet the council marveled and took knowledge that they had been with Jesus. The healed man standing with them was proof positive that they had a power those religious leaders could not touch or duplicate. Because the notable miracle had been done by them and was manifest to all who dwell in Jerusalem, they could not deny it. So they could say nothing against it. Instead, they commanded them to go aside and conferred among themselves, wanting the message spread no further, showing how Satan uses religious people to stop the truth.
And beholding the man which was healed standing with them, they could say nothing against it.