Picture one person standing just behind another and watching over them — close enough to step in, far enough to let them try. That watching is the whole word. From where the younger person stands it feels like being taught and looked after; from where the older one stands it feels like a duty they are carrying. Both meanings of tutelage can be thought of as the same scene viewed from the two sides.
From Latin tūtēla, a watching or guardianship, from tuērī, to watch or guard, with the ending -age. The idea of someone watching over you is inside the word from the start.
這個字來自拉丁文 tūtēla（看守、守護），再往前是 tuērī（看、守），字尾是 -age。也就是說，「有人在旁邊看著你」這個意思，一開始就在這個字裡面。
Wiktionary entry for tutelage, supplied in this packet (source_ref kaikki:3f6f69a190036ae4:671647653:11442): From Latin tūtēla (a watching, guardianship, protection) + -age, from tuērī (to watch, guard). See tuition.
From the picture
看顧別人的那份責任
同一個畫面換個角度：現在說的是站在後面那個人。他要為對方的教育、行為甚至財產負責，所以字的重心從「學到什麼」移到「誰要負責」，語氣也更接近法律和制度。
noun · C2
The duty of looking after someone and being answerable for their education, their behaviour or their property, as a parent or a legal guardian is.
監護（責任）／看管
noun · C1
The teaching, training and care you receive while you are in the charge of one particular person, especially in the phrase under someone's tutelage.
指導／受教（在某人門下）