Is it permissible for my brother to justify his insulting and cursing me, knowing that this happens constantly as a form of jest, and will I be sinful because of it?

Slandering and insulting a Muslim are forbidden, based on the Prophet's (peace be upon him) sayings: "Abusing a Muslim is فسوق (disobedience/wickedness) and fighting him is disbelief," and "A Muslim is one from whose tongue and hand the Muslims are safe." A Muslim is far removed from obscenity and vulgarity. The Prophet (peace be upon him) used to joke but would only speak the truth.