Someone who's extremely stubborn, refusing to change their mind even when it's in their best interest, is pigheaded. It's almost impossible to get a pigheaded person to listen to your advice.
If your brother refuses to wear a winter coat on a freezing winter day, obstinately sticking to this decision even after he steps outside and starts shivering, he's pigheaded. While the original meaning of this adjective was, briefly, "having a head resembling a pig's," it's long been used to mean "stupidly stubborn." This figurative meaning comes from the reputation of pigs as being stubbornly willful.