to give in, to admit defeat
Depois de muita discussão, ele finalmente deu o braço a torcer e admitiu que eu tinha razão.
After a long argument, he finally gave in and admitted I was right.
Dar o braço a torcer ("to let one's arm be twisted") means to give in and admit one was wrong, while its negative, não dar o braço a torcer, means to stand firm. The image is bodily: an arm being wrenched stands for being forced to yield, so refusing it means resisting.
Sources: RTP Ensina, Escreva.ai.
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