不甘

不甘 carries an emotional charge of pride or stubbornness - refusing to settle. Common collocations: 不甘失败 (unwilling to lose), 不甘落后 (unwilling to fall behind), 不甘寂寞 (unwilling to stay quiet/out of the spotlight). The fuller form 不甘心 (bùgānxīn) is even more common in conversation.

memory

甘 originally pictured something sweet on the tongue - by extension 'to find palatable, to accept willingly'. So 不甘 is literally 'cannot swallow it', a vivid match for 'refusing to accept'.