It's not uncommon for a person to be attracted to somebody when they first meet, but then settle into a more friendly relationship once they get to know each other. The initial attraction is just based on physical appearance, because that's the only thing you know about a person on first meeting them. That 'attraction' doesn't always remain once you've got to know the person and start to think of them as a friend.
To give it a more literal, non-in film explanation, there wasn't really any room for a relationship between Robin and Batgirl in this movie. There was a lot going on. Batgirl was introduced and two villains taking up a lot of the run time. A big part of the story involved the men falling for Poison Ivy's hypnotic powers. It would've been hard to fit in a romance between Robin and Batgirl without it feeling forced.
Remember also, Robin wasn't given a lot to do in Batman Returns, he was just being introduced. Maybe the Robin / Batgirl relationship would've evolved if they'd made another sequel.
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