Krishna steps from the ritual fire into the family. I am the father of this world, and the mother, and the grandfather, and the one who sustains it all. I am what must be known, the purifier, the sacred syllable Om, and the three Vedas — Rig, Sama, Yajur.
Notice how Krishna claims both roles — father and mother. Not one or the other. The divine holds the firmness of a father and the tenderness of a mother at the same time. And then 'pitamahah' — grandfather — the one who has been here even longer, who holds the family's memory.
By naming the three Vedas, Krishna declares himself the very source of knowledge. The Vedas are not separate from him. This shloka deepens the list from 9.16: there, it was every element of ritual; here, it is every relationship and every tradition.