If by chastise, punishment is meant, the simple and blunt answer is No! We are not to chastise our brethren since we are not their parent. Only the Lord, our mutual Father, has the right and responsibility to chastise a brother or a sister.
But we assume, the questioner means should a woman bring a wrong-doing to the attention of a man? Of course, this is a very honorable question, and the Lord has given us the answer in Matthew 18:15, “If your brother sins, go and show him his fault in private; if he listens to you, you have won your brother.” (NAS)
The passage continues to discuss how to resolve a problem if he does not respond properly.
Our heart attitude is very important when we confront a problem. Ephesians 4:15 (NLT), “we will speak the truth in love, growing in every way more and more like Christ.”
Whenever we are hurt and our emotions enflamed, speaking in love is almost impossible. Therefore, until we calm down and can talk in a loving, respectful manner, we should wait. Tell the person that the problem is very important but you would prefer to discuss it later. Then physically remove yourself from the argument. Wait – minutes, hours, perhaps days – and ask God to help you to make your words loving and wise.