One of the original arguments from the oriental legalism the spawned the punishment, coming from the culture of the time, was that for serious criminals who were caught rather than turned in by family the family almost certainly knew and were sympathetic to their crimes, and enacting capital punishment on the criminal was highly likely to create a treasonous blood feud in the other family members against the government. So their punishment was immediately extended to their presumed sympathisers to cut off a cyclical disruption to the country's "harmony" by letting their resentment fester into inevitable reprisals. It was explicitly anti-revolutionary as well as judicial.

A father who sympathised with his son's desire to kill cops rather than accept the legal process, so much so that he immediately went out to extra judicially murder a random cop when his son was stopped is an example of the assumptions behind the familial punishment being proven right.

I didn't even say that it was the right choice, obviously morally a legal system should not rely on assumptions, even though practicality demands it in every legal system in the world. I just said that proving the assumptions right was how you get people agreeing with the concept.