What does Matthew 12:34 mean?

Christ is thoroughly and righteously condemning the group of Pharisees. These legalistic religious leaders have accused Him of getting His power to cast out demons from Satan (Matthew 12:24). They are so committed to rejecting Jesus as the Messiah that they would rather glorify Satan's power than acknowledge that God is working through His Son! In the previous verse, Jesus compared the Pharisees to bad trees. This was proven by their bad "fruit:" rejecting and accusing Him.

Here, the criticism intensifies. Jesus repeats what John the Baptist called a group of Pharisees and Sadducees in Matthew 3:7. The word "brood" means offspring (John 8:42–44), so Jesus is calling the Pharisees children of snakes. This associates them with Satan, often pictured as a serpent in Scripture, beginning in Genesis 3. These critics have accused Christ of using Satan's power—but truth is they are the ones aligned with Satan and against Jesus.

The question asked here is rhetorical—it's making a point. In the same way that a bad tree is incapable of growing good fruit, a person committed to hate for Christ can't speak spiritual truth. Jesus bluntly calls these men evil. Good words cannot come out of evil hearts. The Pharisees words about Jesus and Satan showed to everyone their true, evil selves.

This Scripture reveals a blanket principle for all people: our words always eventually reveal what's going on inside of us. There's no such thing as an unimportant act, or an unimportant word (Matthew 12:36).