You can think of a debt being settled and the slate wiped clean, so that a person can walk away with nothing left hanging over them. In court the debt is a charge, and wiping it clean means the person is free. Turn the same idea on yourself and it becomes the part you owed on the day: you gave it, and you can walk away from it too.
The source traces acquit to Old French aquiter and Medieval Latin acquitāre 'to settle a debt', from ad- 'to' plus quitare 'to free' — a doublet of quit. Settling and freeing sit inside the word from the start.
來源資料說 acquit 來自古法文 aquiter 和中世紀拉丁文 acquitāre（把債務結清），由 ad-（朝向）加 quitare（使自由）組成，跟 quit 同源。「結清」和「放開」這兩件事，從一開始就在這個字裡面。
Wiktionary entry for acquit, etymology: Middle English aquī̆ten, Old French aquiter, Medieval Latin acquitāre (“to settle a debt”), from ad- + quitare (“to free”); doublet of acquiet, related to quit. (packet ref kaikki:3f6f69a190036ae4:527864149:51832)
From the picture
把自己該交的那一份交出去
同樣是「把該負的交代完」，只是這次要交代的是自己在場上的表現。來源資料裡 acquit 也有「把債結清、把責任履行完」的舊意思，這一層就沿著那條線長出來。
verb · C1
If you acquit yourself well or honourably, you do something difficult well, especially something you are doing for the first time while other people are watching.
表現得宜、表現出色
verb · C1
If a court or a jury acquits someone, it decides at the end of a trial that the person is not guilty of the crime they were charged with.
判…無罪