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Interesting response Cary but I doubt that from his parent's point of view this is about "victory" or "defeat," or making their son miserable about his partner as you seem to suggest.
You may not realise this but "carrying on the family line" is not simply a genetic, social or material issue in Asian societies (I am an Asian myself) but part of huge spiritual and "religious" issues. For example, death and remembrance rituals require direct heirs and without them, the soul is not considered to be at peace or "pass on."
For the parents then, the biggest problem is the issue of children. I agree with the other poster: the lady needs to talk about it (has she even discussed it with her partner?) with them; and then may be work at having children.
I realise the above goes COMPLETELY against the American cultural values that place the individual and their wishes of paramount importance. And she may not WANT to have children. But that is something she needs to figure out in context of this relationship because those are the parameters - culturally, emotionally AND realistically.
From my own perspective of course this relationship is doomed. It may end now or in five years time. The lady's description of her partner's culturally engrained sense of responsibility and concern for his parents (and their wishes/feelings etc) as "infantile" and weak suggests a lack of respect and understanding on her part for him, his family, and his cultural values. THAT is a REAL indicator that this one is dead in the water.
And in any case: If this guy hasn't talked to his parents, are you sure he is interested enough in the relationship? If this couple hasnt talked about issues (like children which his parents want for him), is there a relationship? Asian men (and women) balance family responsibilities and partners all the time. Seems like he isn't convinced enough about his partner to even try sorting things out with his parents.....