Demur
Etymology
From Old French demorer, "to linger, delay," from Latin demorari, "to delay," built from de- plus morari, "to delay," from mora, "delay." The original sense was simply to hold back or tarry; English narrowed that hesitation into the polite act of voicing a doubt or objection.
verb · /dih-MUR/
To raise an objection or show reluctance, often politely.
What it names
The genteel word for hesitating or pushing back — a mild, courteous "I’m not sure about that" rather than a flat refusal.
Example
When they proposed him for chair, he demurred, saying others were better suited.
Related idea
Object states outright opposition; to demur is softer — a hesitation or reservation more than a refusal.