Arjuna's argument widens beyond the personal. When a family is destroyed, he says, the ancient traditions passed down through generations are lost forever. And when dharma is lost, adharma — unrighteousness — takes over the entire family.
Think of a village where the elders pass away one by one. With them go the old ways — the rituals, the festivals, the unwritten codes of how to live with honour. The younger generation, left without guidance, drifts. They no longer know what was done or why. The thread that connected one generation to the next is cut.
Arjuna is building a chain here: war leads to the destruction of the kula, which leads to the death of dharma, which leads to the rise of adharma. Each link follows from the one before. And at the end of this chain, nothing good remains.