Considering that there are some asexuals who have romantic and potentially marital interests without sexual interests, and significant subcultures in which sex before marriage is considered completely inappropriate, I don't think that's a fully general disanalogy.

Edit: Or to put it differently, I think you're presupposing that "the point" of dating is to have a relationship that involves sex. Perhaps conflicting presuppositions of this nature are part of the problem in the case of the story and the reverse case I suggested. Illustration: our heroine Darla arranges a date with some guy Bob. Darla thinks the point of dating is to find a spouse and Bob thinks the point of dating is to find someone with whom to have a sexual relationship. Darla starts talking about how to divvy up chores in a marriage and he freaks. Darla is confused, because isn't "the point" of dating to find a compatible spouse? But she backs off because she doesn't want to upset him. Then he starts insinuating that he'd like to have sex. She freaks. He's confused, because isn't "the point" of dating to find someone to have sex with? Now they're both confused: Bob has no idea why Darla wouldn't want to sleep with him when she just brought up marriage, for crying out loud - what, is she proposing that they could set up housekeeping and have separate beds and conceive the three children she wants via IVF? Darla has no idea why Bob would bring up sex on a first date - or at all, really, since obviously he has no interest in sticking around, doesn't like her enough to find out if she's a prospect for anything really long term, and why would he expect her to react well to the proposition when it's plain from his behavior he only views her as a piece of meat?

Now, Darla never envisioned a sexless future and Bob doesn't dislike Darla - perhaps he isn't even fundamentally opposed to the idea of marriage. They just have very different ideas about what order to start planning for the two events.