Something that's wrongheaded is foolish, misguided, and stubborn. A wrongheaded politician might run for president despite polls showing there's no way he can win.
A wrongheaded entrepreneur may go ahead with her plans to open an ice cream shop for dogs despite being advised not to by everyone she knows. You might feel angry about a judge's wrongheaded decision in an important court case. Anyone who uses bad judgement is wrongheaded, especially when the mistake seems obvious. The adjective wrongheaded has been around since the 1730's.