It is perfectly natural for a person who may never see their home again to weep for their parents and family, and this is the view of Rabbi Eliezer.
Rabbi Akiva, however, as reported in the Sifrei, suggests that “father and mother” in this case is a metaphor for the woman’s idols.
This view derives from Jer. 2:27, where an idolater is recorded to have said to a piece of wood, “You are my father”. The prophet is mocking idolatry, which takes a block of wood or stone and turns it into an object of worship.
The same idea is developed in detail in the Hallel psalms and recurs throughout Biblical literature, which constantly wonders how any sensible person can possibly take idolatry seriously.
Nonetheless, the passage about the prisoner of war has a deeper connotation. It indicates that what a person misses is not only their mother and father, but the ways, values and habits of their background.
One of the lessons we learn is that a convert to Judaism can never drop everything overnight and in Billy Graham fashion make an instant decision to be born again. Human nature and experience do not work like that.
Becoming Jewish is a gradual process of integrating into Jewish beliefs and commitments… and of unlearning priorities from the past.