Picture one process making one thing. Beside the thing everyone wanted, something else keeps coming out, without anyone planning it. That side thing is the by-product. Once you can see that picture in a factory, the same picture carries straight over to what people do: you act for one reason, and something extra falls out beside the reason.
The word is literally by- plus product, and product goes back to Latin prōdūcere, to lead or bring forth. Read together, it says: the part that was brought forth beside the main thing.
字面上就是 by-（在旁邊、附帶）加上 product（產品）。product 這條線更早來自拉丁文 prōdūcere「引出、生出」。合起來可以讀成「在主要的東西旁邊，被一起引出來的那一份」，跟今天的兩個用法都對得上。
Wiktionary (kaikki extract), by-product: 'From by- + product.'; source_ref kaikki:3f6f69a190036ae4:1121978363:20964
From the picture
做事情順便帶出來的結果
把生產線的畫面整個搬到行為上。你做一件事是為了某個目的，過程中卻另外生出一個你沒打算要的結果——這個結果站的位置，就跟工廠裡那堆木屑一模一樣。這是一種理解上的連結，不是說這個用法比較晚才出現。
noun · B2
An extra result of something you do or something that happens, which nobody planned and nobody was aiming for. It can be a good result or a bad one.
附帶的結果
noun · B2
Something extra that is made while something else is being made, in a factory or by a natural process. It is not the thing anyone set out to make.
副產品