wrongheadedly

In pigheaded fashion

In a stubbornly misguided manner, persisting in error despite evidence or reason: She wrongheadedly insisted on taking the shortcut that added an hour to the trip.

The word implies not just being wrong but clinging to wrongness with conviction.

stubbornly

obstinately

In an unyielding manner

doggedly · inflexibly · unyieldingly · adamantly · willfully · headstrongly · intransigently · perversely · obdurately · tenaciously

misguidedly

foolishly

In an unwise manner

injudiciously · imprudently · ill-advisedly · confusedly · blindly · naively · ignorantly · simplistically · unsoundly · fallaciously

irrationally

unreasonably

Beyond logical limits

nonsensically · preposterously · ludicrously · incoherently · mindlessly · unthinkingly · groundlessly · unjustifiably · indefensibly

recklessly

impulsively

Without prior deliberation

thoughtlessly · hastily · precipitously · impetuously · incautiously · indiscreetly · inadvisedly · shortsightedly · unthinkingly

Opposites
correctness of judgment/approach

wrongheadedlyrightly

In correct fashion

correctly · soundly · wisely · sensibly · judiciously

openness to reason/evidence

wrongheadedlyopen-mindedly

With willingness to consider

receptively · reasonably · flexibly · thoughtfully · fair-mindedly

Family

wrongheaded, wrongheadedness

Familiarity
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Used worldwide · Timeless · Abstract · Negative · Everyday, not technical · Rated G