Cathy is right: love is youth. For someone who is afraid of getting old, having a relationship with a younger person is the best way to forget about their age. This is a paradox because Cathy is obsessed with the passing of time and she's suffering as a result.
It's likely that Darren is fascinated by this relationship with a woman the age of his mother, as well as satisfied that other women and Cathy's friends are showing interest in him. It's also likely that he finds this relationship reassuring. He might think it's unlikely that she'll leave him for someone else so he's able to draw the relationship out for as long as he likes.
As for Cathy, Darren probably plays several roles in her life: he's the child she can mother, the possessive and jealous father, and the lover. All rolled into one! And one of the virtues of love is that it's timeless, which is reassuring for a woman who's afraid of aging.
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