hesitation; reserve; hindrance
Refers to holding back out of respect, diffidence, or fear of causing trouble. Often used in the set phrase 憚りながら (with all due respect). The hindrance nuance is less common as a standalone noun.
Euphemistic, somewhat dated term for a toilet or washroom, derived from the idea of a place one hesitates to enter or mention directly. Still understood but less common in modern casual speech.
With all due respect, I believe that plan may be unreasonable.
Out of diffidence and reserve, he couldn't bring himself to voice his own opinion.
In old inns, the washroom was often shared.
with all due respect; I venture to say; excuse me, but
Standard kanji spelling. The kanji 憚 is not a jōyō kanji, but this form is common in set phrases.
Kana spelling is common in everyday writing, especially for the washroom sense.
Derived from the verb 憚る (はばかる, to hesitate or be wary). The noun form 憚り nominalizes this sense. The washroom meaning is a euphemistic extension.