Why does transitive relationships fail?

The most common reason transitive relationships fails: Assuming all relationships are transitive when most are not. You trust your friend, and your friend trusts a stranger, so you extend trust to the stranger — but your friend's criteria for trust may be entirely different from yours. You see that your manager reports to the VP and the VP reports to the CEO, so you assume your priorities are aligned with the CEO's — but the relationship 'reports to' does not make 'shares priorities with' transitive. The deeper failure is treating the word 'relates' as if it names a single thing, when in reality different types of relationships have radically different transitivity properties. 'Is taller than' is always transitive. 'Is a friend of' almost never is.

The fix: Map one transitive chain in your own life. Pick a relationship that matters to you — professional, personal, or intellectual — and trace how you arrived at it. Write down the intermediary: who introduced you, what event connected you, or what piece of knowledge led to the next. Now extend the chain one step further back: how did you come to know the intermediary? You should have at least a three-node chain (A → B → C). Then answer two questions. First: would the A-C relationship exist without B? Second: are there other transitive chains in your life where a critical intermediary is a single point of failure — where if that one node disappeared, the downstream relationship would never have formed? Identify at least one such chain and write a one-sentence assessment of its fragility.

The underlying principle is straightforward: If A relates to B and B relates to C there may be an implied relationship between A and C.