The protagonist of that story is a Hollywood Rationalist. She doesn't really have any purpose behind most of her actions; it seems that (at least at the beginning), the only reason she uses rationality is to antagonize other people and make conversations awkward. Unsurprisingly, she becomes unhappy.

In that particular context, since "I'd like to take you to a show" and "I'd like to have sex with you" both demonstrate one common fact, that he wants to have sex with her, she considers them as being totally equivalent. Though it's still unclear why she would find the statement, "I'd like to have sex with you" offensive, given how she otherwise thinks, but since her purpose seems to be antagonizing people, it fits.