One way to hold this word: draw your family tree, then draw a wedding ring around two of the names. Every line inside the ring was made by a wedding, not by birth. A -in-law is a man who ends up standing where a would stand on that tree — same generation as you, close enough to sit at the family table — but the line that put him there is a marriage. The word never says whose marriage it was. That is why the same three cover your wife's , your sister's husband, and the man who married your wife's sister, and why speakers so often add one short sentence afterwards to say which line they mean.
From the word’s history
Middle English brother-in-lawe: brother plus -in-law, literally a brother by law rather than by birth. The -in-law part is exactly what the modern core image keeps: the line on the family tree was drawn by a marriage.
中古英文寫作 brother-in-lawe，就是 brother 加上 -in-law，字面上是「法律上的兄弟」。今天的核心畫面留下的正是 -in-law 這半邊：家族樹上那條線是婚禮畫的，不是血緣畫的。同一組還有 mother-in-law、son-in-law。
Wiktionary, entry 'brother-in-law' (kaikki:3f6f69a190036ae4:115795817:159412): 'From Middle English brother-in-lawe; equivalent to brother + -in-law.'
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