Paul had been arrested for his own safety, but now the Roman authorities wanted to find out exactly what the problem was. The Jewish High Council was told to sort it out.
They never really gave themselves a chance:
Acts 23:6 Paul realized that some members of the high council were Sadducees and some were Pharisees, so he shouted, ‘Brothers, I am a Pharisee, as were my ancestors! And I am on trial because my hope is in the resurrection of the dead!’
There’s nothing like an ideological difference to get people arguing, and that’s what they did: the Pharisees started defending Paul; the Sadducees became angrier. The High Council rioted:
Acts 23:10 As the conflict grew more violent, the commander was afraid they would tear Paul apart. So he ordered his soldiers to go and rescue him by force and take him back to the fortress.
It probably wasn’t their finest hour.
Tactically, it meant Paul was taken away from the jurisdiction of the High Council, and it showed the commander the petty, religious nature of their problem with him. On the other hand, it also led to a (unsuccessful) conspiracy to kill Paul, and it was the start of his journey to a Roman gaol.