Using authority to lead may achieve your goal but it creates unintended side-effects, nearly always counter to your goals. To you personally too.
This scene in Lincoln illustrates how the side-effects can last centuries. I long wondered why people resist accepting the Civil War. Why wouldn’t they celebrate ending slavery?
When you motivate someone through authority, you are making them do something they don’t want to do. You’re threatening a worse outcome if they don’t do it—firing, a bad grade, a spanking, jail, garnishing wages, etc—implying that being with you can be even worse. What are you presenting about yourself?
Leading through authority motivates people to undermine your authority and resent you.
This scene dramatizes Lincoln’s strategy of passing a constitutional amendment to institutionalize his view. Even people in the south who agree with him now have to follow his amendment under threat of breaking federal law, meaning under threat of invasion and war.
This scene finally illustrated to me why people resent the outcome of the Civil War. People don’t resent ending slavery. They resent someone leading them through authority.

For all I know Lincoln had no better option. I’m not second-guessing him. I’m only suggesting that behavior we see today results from authoritarian decisions he did then.
When you lead through authority, you’re provoking people resenting you and seeking to undermine your authority too.