Thank you for the question about Festus statement to Paul, “In the Bible in the book of Acts, why did Festus raise his voice to Paul and say, “Paul, thou art beside thyself; much learning doth make thee mad”?”
The Scripture does not state the reason why Festus made his statement of Paul being insane.
Here is a thought for the reason for Festus’ statement to Paul:
Festus could not agree to Paul’s belief and logic in arguing that Jesus arose from the dead. In Festus’ mind, that is an impossibility. He has never seen anyone coming back alive from the dead. He has heard rumors of such things being done by Jesus but that is just rumors. It is an exaggeration in his mind.
Festus heard that Paul was a Pharisee and believed in the resurrection. He may have concluded that Paul was delusional in that this Jesus appeared to him on the Road to Damascus. His firm belief in the Torah and his “delusional” experience drove Paul to be insane in his overzealous belief of the resurrected Jesus. Festus heard Paul’s testimony and it was to incredible to believe.
The other possibility is that Festus may have been under conviction of the Holy Spirit. He heard Paul’s testimony but to end his testimony and his own knowledge of the Torah, he shouted those words so as to not to give his attendees the idea that he was convinced that the testimony is genuine. It was a deflection method. He could not be seen as being convinced since the Jews and royal officials were present in that court hearing.
Which one am I leaning toward? The latter is my view for Festus words to Paul and Paul’s response in Acts 26:25–29 would tend to reflect that Festus was under conviction. The text says this, “I am not insane, most excellent Festus,” Paul replied. “What I am saying is true and reasonable. 26 The king is familiar with these things, and I can speak freely to him. I am convinced that none of this has escaped his notice, because it was not done in a corner. 27 King Agrippa, do you believe the prophets? I know you do. 28 Then Agrippa said to Paul, “Do you think that in such a short time you can persuade me to be a Christian?” 29 Paul replied, “Short time or long—I pray to God that not only you but all who are listening to me today may become what I am, except for these chains” (NIV).
SUMMARY: Both Festus and King Agrippa were under conviction of the Holy Spirit by Paul’s testimony. The choice becomes will they believe or not.
For more perspectives: