bù​gòng​dài​tiān

absolutely irreconcilable

Senses

不共戴天 bù​gòng​dài​tiān (also bú​gòng​dài​tiān) absolutely irreconcilable

Literally "not living under the same sky"; describes an extreme hatred between enemies who cannot both exist in the world, often used in the context of seeking revenge for a murdered parent.

References

synonym 誓不两立/誓不兩立 不共戴天/不共戴天
synonym 令人切齿/令人切齒 不共戴天/不共戴天