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.

Definitions of pigheaded
  1. adjective
    obstinate and stupid
    synonyms: bullet-headed, bullheaded
    obstinate, stubborn, unregenerate
    tenaciously unwilling or marked by tenacious unwillingness to yield
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