obstinately

/ˈɑbstɪnətli/
adverb
  1. In a way that shows stubborn refusal to change one's opinion or course of action.
    • She obstinately refused to apologize, even when she knew she was wrong.
    • He obstinately continued to argue his point long after everyone else had moved on.
    • The old man obstinately insisted on walking to the store despite the rain.
Antonyms