All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is an obligation upon a true Muslim to avoid speaking bad about others honor, be they men or women, insult or call them names. This is since The Messenger of Allah (PBUH) said, "A true believer is not involved in taunting, or frequently cursing (others) or in indecency or abusing." {At-Tirmidhi}. In fact, Sharia came to preserve five necessities: religion, intellect, honor, wealth, and life, and banned any aggression against them. There are many an evidence on this. For example, The Prophet (PBUH) said, "A Muslim is the one from whose tongue and hands the Muslims are safe." {Transmitted by Muslim}. In his commentary on this report, An-Nawawi said, "It means not harming others with word or action. The hand is mentioned in particular because most actions are done using it." {Shareh An-Nawawi Ala Muslim, Vol.2:10}.
It was mentioned in the book {Fayed Al-Khadeer, Vol.6:271}: "Harming a Muslim indicates a shortage in the faith of the person who commits such act. There two types of harm: Physical and none Physical. Physical harm is, for example, taking others wealth through theft or looting. Non-physical harm is embodied in envy, hatred, arrogance, harshness, thinking ill of others, and the like.
In addition, a Muslim is commanded not to talk about others in a manner that they don`t like (Backbiting}. Allah the Almighty says {What means}: "And spy not on each other behind their backs. Would any of you like to eat the flesh of his dead brother? Nay, ye would abhor it...But fear God: For God is Oft-Returning, Most Merciful." {Al-Hujurat, 12}.
An-Nawawi said, "Chapter on prohibiting backbiting and calumny: These are the ugliest and most widespread of sins, so I began with them as a warning. As for backbiting, it is talking about your brother in a manner that he doesn`t like…..As for calumny, it is conveying false statements to people to cause them to get on each other's necks. According to scholarly consensus, both are forbidden, and texts of Sharia are agreed on that as well.
An exclusion to this general rule (Al-Asl) is that it is permissible to utter evil words out loud if a person is wronged; however, this shouldn`t exceed the permitted limits because the general rule is that this is forbidden." {An-Nisa`, 148}.
However, a Muslim should adhere to the morals celebrated in Islam and avoid lying and falsehood and not to be carried away by the desire to slander and take revenge. Allah the Almighty says: {What means}:"O ye who believe! stand out firmly for Allah, as witnesses to fair dealing, and let not the hatred of others to you make you swerve to wrong and depart from justice. Be just: that is next to piety: and fear Allah. For Allah is well-acquainted with all that ye do." {Al-Ma`idah, 8}.
In conclusion, as a general rule, it isn`t permissible to insult others; however, it is permissible for the wronged to claim their right by the legal means generally accepted in the country where they are staying. And Allah the Almighty knows best.