Male and female roles are not symmetrical but instead of a different nature, different in nature the one from the other.
The way the complementarity of the sexes is (in contrast) usually (but misleadingly) described is a very 'masculine' way (suitable to public discourse, by analogy with societal policy arrangements) - for instance that The Man is 'in charge of' X and The Woman 'in charge of Y' (e.g. the idea that Woman is in charge of House and Family, and Man ICH The Family Economy and Foreign Policy) - but this never rings true, even with respect to humans.
And even less so with gods - since any such division seems to invite unification as one being; just as any 'division of powers' tends to collapse into a unity of power.
But if the reality is that the complementarity is of natures and qualities rather than domains of jurisdiction, then that seems closer to reality for humans, and more comprehensible for deities.
If one being is of a certain nature and another being of a different and complementary nature - then these natures cannot be united in a single being - because they are incompatible.
If you think of the character of the ideal mother and the character of the ideal father - these two simply cannot be combined in a single being; because many of the perfections of the one are opposed to the other.
(Just think of actual examples of the best of good families - if you know any.)
A hybrid mother-father is not, in fact, a combination of mother and father but necessarily something else altogether (most likely an averaged compromise - inferior to either individually; or something which oscillates from one to the other nature - and therefore partakes of the inhuman).
This argument is simply at the level of common sense and common experience.
An androgynous being does not combine the man and woman but is an intermediate average; and neither does a hermaphrodite.
There is, in fact, nothing that combines the male and female in a full and real sense.
So, in trying to understand, define, formulate ideas about Mother in Heaven - I think we must beware of trying to impose quantitative symmetries which would not be applicable to earthly humans.
An analogy would be a Great Man - a great political or religious leader, a great creative genius - someone who had personally vastly influenced public life ... Imagine (as sometimes happens) that the Great Man always insists, and with perfect truth, that 'I owe it all to my Wife', that he 'could not have done it without my Wife'.
Now if we tried to understand this truthful statement in terms of the Great Man's public works we would be missing the point completely - that would be to regard the Great Man's wife as merely some kind of servant - yet that is clearly not the situation; it is not what is implied by the truthful statements of the Great Man himself.
Typically, it is not possible for an outsider to know what is meant by the Husband's truthful statement 'I could not have done it without her. The Wife's work is outwith the public domain, hidden from external view - it is absolutely real and solid and yet at the same time somehow covert, implicit: a Wife's work is a mystery in a way that the Husband's work is not a mystery.
My guess is that something very similar applies to Mother in Heaven. The role and function of God the Father is primarily understandable because it is public, outward, creative; but the role and function of Mother in Heaven is solid and yet mysterious.
Mother in Heaven's role is fundamentally and intrinsically mysterious but not for any esoteric or difficult to understand reason; but 'simply' in the same way and for the same reason that any Wife's role may be mysterious in relation to the attainments of any Great Man: real and absolutely necessary - yet opaque to the external eye.