Jesus kept silent and answered nothing. - Mark 14:61
Sometimes silence is the best response to a false charge. At other times we must speak up.
When false witnesses accused Jesus as He stood before the Sanhedrin, He "kept silent" (Mark 14:53-61). Defending Himself would have been useless. Furthermore, He was fulfilling the prophecy of Isaiah 53:7. But earlier in His ministry, Jesus rebuked the Pharisees, challenging them to prove that He sinned (John 8:13-59).
A pastor resigned from his church because a few members made untrue statements about him. He thought it unchristian to defend himself, and in some instances it is. But in this case, the troublemakers needed to be confronted and their false charges refuted. He should have urged them to repent or face church discipline.
Saying nothing may allow wrongdoers to go unchallenged in their evil ways. But if God's Spirit leads us to remain silent, or if we want merely to try to salvage our wounded pride, then we should hold our tongue.
Are you being falsely accused? If you discern that it's futile to argue, or if your pride has been hurt, ask God for grace to say nothing. But if you feel concern for the wrongdoers and want to see justice done, speak up! - Herbert Vander Lugt
Silence can be valuable; dont break it unless you can improve on it.