What does Luke 21:15 mean?
Jesus is explaining what the church and the world will experience before He returns at the end of history (Revelation 19:11–16). Specifically, He is warning the disciples how they will be persecuted. They will be kicked out of the synagogues, imprisoned, and forced to defend themselves before political leaders, even kings (Luke 21:12).God will take advantage of their persecution. He will orchestrate opportunities for His followers to share the gospel before these leaders (Luke 21:13). Peter and John will be taken to the Sanhedrin (Acts 4:1–6). Paul will face the Sanhedrin, two governors, a king, and possibly Caesar (Acts 23:1; 24:10; 25:12, 23).
But Jesus tells them not to over-prepare. He tells them not to write out a defense beforehand (Luke 21:14). They are to trust that the Holy Spirit will give them the right words to say; their years of teaching and personal diligence will fill in the rest.
This strategy works. The Sanhedrin has no counterargument to Peter and John's testimony and resorts to bullying (Acts 4:13–21). When the Sanhedrin finds the disciples have been ignoring their order to not teach Jesus' resurrection, they become angry because of the insubordination, not because they don't believe the disciples (Acts 5:17–40). The Sanhedrin doesn't bother listening to Paul's defense and instead finds the slightest offense as an excuse to strike him (Acts 23:2–5). Felix knows Paul is innocent but keeps him in prison because he wants a bribe (Acts 24:22–26). King Agrippa is also moved by Paul's testimony but follows his hard heart instead of what he knows is the truth (Acts 26:27–29).
Jesus tells the disciples that the Holy Spirit will give them words that cannot be contradicted. He doesn't tell them their words will always reap rewards. Even the best argument has no effect when the listener refuses to accept it (Matthew 13:15).