पिताऽहमस्य जगतो माता धाता पितामहः।वेद्यं पवित्रमोंकार ऋक् साम यजुरेव च॥
pitāham asya jagato mātā dhātā pitāmahaḥvedyaṃ pavitram oṃkāra ṛk sāma yajur eva ca
Word by word
The verse says
I am the father of this world, and the mother, and the one who holds it, and the grandfather. I am what is to be known, the purifier, the syllable Om, and the three Vedas.
In plain words
Mother is in the list, in the same breath as father, with nothing marking it as unusual.
Then grandfather, which puts two generations of the family in one line.
He is not being described as a ruler here. He is being described as a household.
Where you've felt this · in parenting
Your friend was raised by his mother on her own. The one who was strict about homework was also the one who sat on the edge of the bed afterwards and heard about the argument at school. It was not two people taking turns. It was one person being both things inside the same hour.
Going deeper
Putting mother and father in a single line, with neither one qualified, is more striking than a modern reader may notice.
This was written in a world with a firm view about which of those roles carried authority. The verse spends no time on the point and makes no argument for it. Both words simply appear, side by side, in a list of what he is.
The word for holder is worth having as well: the one who bears the weight, keeps the thing going, is responsible for its continuing to exist.
What that offers is a choice of language rather than a doctrine. If the picture of God as a father has never done anything for you, or has done something unhelpful, the verse itself supplies the alternative. It is not a concession. It is in the original line.