https://rabbifriedlander.wordpress.com/2020/01/12/the-tefillin-of-women-is-modesty-and-the-modesty-of-men-is-tefillin/A woman is rewarded, as a man cannot be, by dressing modestly in public to save others from potential sin.
Men are rewarded as a woman cannot by putting on that which binds to them the concept that there is someone greater than them and therefore dedication to competition and conquests against others alone cannot define life for, in truth, they can never achieve absolute supremacy. God already won that title forever.
Whereas women do not need such a wake up call due to their intrinsic superior understanding of humanity and its limitations.
That is why for women Tefillin is only optional and for men it is required.
That is why for women Tefillin cannot prove their righteousness, but by thinking of others before themselves whenever they choose clothing, they become just as elevated as men with Tefillin. Generally speaking this is a much greater calculation, effort and even potential sacrifice when done by a women whose natural affinity for the complexity of fashion is comparably much greater than such capacity within an average man. The desire to wield this skill set is thus also greater than that of most men. Thus this becomes the proving ground of feminine sincerity of placing God first and their own agenda second.
Whereas crafting Tefillin is extremely complex and is an intellectual counterpart to complexity in fashion. This creates a symbol of modesty before the angelic court in Heaven. In other words, from this perspective, Tefillin is kind of a spiritual power up to enable a man to equal the holiness of a modest woman.
Both prove their humility in an obvious way and thus publicly honor the Blessed Creator greatly, each in their own way.
Therefore we can say that the Tefillin of women is modesty, and the modesty of men is Tefillin.
And thus we have it that Public Morality for a Jew begins here. Men dress modestly and put on tefillin and women dress extra, extra modestly.