Remonstrate
Etymology
From Medieval Latin remonstrare, "to demonstrate, point out," from re- (intensive) plus monstrare, "to show," from monstrum, "an omen, a showing." The core idea is to show something plainly; in English it narrowed to showing someone the error of their course, forcefully and in protest.
verb · /rih-MON-strayt/
To protest or argue against something by forcefully pointing out objections.
What it names
The word for earnestly making your case against a decision — laying out, point by point, why it is wrong.
Example
She remonstrated with the board for an hour, detailing exactly how the cuts would gut the department.
Related idea
Protest can be a single loud objection; to remonstrate is to reason at length, marshalling arguments against the thing.