Chinuch Horaah of the Day:
The reason that it was only the candles of Sarah and Rivkah that “remained lit from erev Shabbos to erev Shabbos” – and likewise, the candles of all their descendants, all Jewish girls and women – and that this miracle did not occur when Avraham Avinu lit his candles, is connected with the Torah-ordained roles of men and women in the home.
Our Sages state that the role of a man in the home is מביא חיטין (“He brings the wheat”) – he provides [the basic material for sustenance] in the home, while the task of the wife, “a helpmate to complement him,” is to work with the wheat and turn it into edible food. The way that Hakadosh Baruch Hu established the nature of the world is that “It is man’s way to conquer,” to bring things from the outside into the home. In contrast, of the woman, [Torah tells us,] כל כבודה בת מלך פנימה (“all the glory of the King’s daughter is within”). She is the akeres habayis (“mainstay of the home”), and so her role is inside the home: to work with and transform what is brought in from the outside in such a way that it becomes fit for use by adam (man), until ultimately this sustenance becomes fitting, so to speak, for Adam Ha’Elyon (Hakadosh Baruch Hu).
This why Avraham’s candle-lighting did not cause the candles to physically illuminate the home in a supernatural manner, for there was no connection between candle-lighting and his role
It is specifically Sarah, Rivkah, and all the daughters of Sarah, Rivkah, Rochel, and Leah – all Jewish women and daughters – who are charged with the shlichus and role to be involved with the needs of the home, and work with the physical dimension of the home. They have the mission and power to illuminate the entire home, all the time, through their candles, so that it is recognizable throughout the week that this is a home in which a daughter of Sarah and Rivkah lit a Shabbos candle.
(Likkutei Sichos, vol. 15, pp. 170-173.)