अधर्माभिभवात्कृष्ण प्रदुष्यन्ति कुलस्त्रियः।स्त्रीषु दुष्टासु वार्ष्णेय जायते वर्णसङ्करः॥
adharmābhibhavāt kṛṣṇa praduṣyanti kula-striyaḥstrīṣu duṣṭāsu vārṣṇeya jāyate varṇa-saṅkaraḥ
Word by word
The verse says
When lawlessness prevails, Krishna, the women of the family are corrupted; and when women are corrupted, the mixing of social orders follows.
In plain words
This verse says that social collapse works through women, and that the result is the blurring of caste boundaries.
It should be read for what it is: a fear belonging to a particular society at a particular time, spoken by a man who is falling apart and reaching for received wisdom.
Krishna does not agree with it. He does not disagree either. He never takes it up at all.
Where you've felt this · in parenting
A relative under strain repeats a line about how things were better when people knew their place. You have heard it in that family before. It arrives whole, unexamined, because it was never theirs to begin with.
Going deeper
This verse deserves a plain account rather than a smoothing-over.
What it says is that when order breaks down the women of the family become duṣyanti — corrupted — and that varṇa-saṅkara, the mixing of the social orders, follows. The anxiety is about the purity of lineage, and it places responsibility for that purity on women. It reflects the social world the epic was composed in.
Three things are worth knowing, and all three are simply true of the text.
First, these are Arjuna's words, not Krishna's. Chapter 1 is the collapse; the teaching has not started.
Second, Krishna never endorses this argument. When he answers in Chapter 2 he does not address family purity, tradition or social mixing at all. He treats the whole speech as something to be got past, not debated.
Third, Krishna says something in Chapter 9 that cuts directly against it. At 9.32 he states that women, and anyone of low birth, reach the highest goal by turning to him. That is a different position entirely, and it is his.
A reader is better served knowing this than being handed a translation that quietly softens the line.