Śatapatha Brāhmaṇa ("of a hundred paths") 3.8.2.5

3.8.2.5

atha yatpatnyupaspṛśati | yoṣā vai patnī yoṣāyai vā imāḥ prajāḥ prajāyante tadenametasyai yoṣāyai prajanayati tasmātpatnyupaspṛśati

Then as to why it is the wife that cleanses. The wife is a woman, and from woman progeny is born here on earth; thus he causes that (creature) to be born from that woman; and therefore the wife cleanses (the victim).