First, 倫 lún：this is a combination of 人 person and 侖 which is 亼 chí / ji gathering 冊 books (for those who care: 形聲必兼會意）; the basic idea is thinking, and sorting into categories, specifically age groups.
So the 倫 refers to the relations within the family, first and above all: between spouses, between parents and children, between siblings. By itself, 不倫 means to disregard the boundaries of proper relations, to act outrageously, to betray trust.
A related expression 不倫不類 thoroughly incongruous, mismatched, messed up. Maybe the first scientist to study a platypus might have thought this: it’s a venomous mammal with a bill and lays eggs ~ what’s going on here!?
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