1. What does it mean?
반박불가 literally combines rebuttal with impossibility. In casual comments it expresses emphatic agreement or jokingly presents an opinion as so obvious that no argument is needed.
Also written or said as banbakbulga
2. The nuance
It is often rhetorical rather than a serious claim of proof. Someone can label a favorite snack 반박불가 without everyone actually sharing that preference.
3. Examples
“우산은 비 오기 전에 챙겨야 한다는 말은 반박불가.”
You can't argue with the advice to pack an umbrella before it rains.
“친구가 자기 고양이가 제일 귀엽대서 반박불가라고 했어.”
My friend said their cat was the cutest, and I said I couldn't argue with that.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.