When Batman and Batwoman go out of town, leaving their teenage sidekicks alone and unsupervised, Bat-Girl immediately throws herself at Robin.
Despite the fact that he's a red-blooded teenage boy, and the fact that young Betty Kane is a pretty teenage girl, Robin rebuffs her.
Another woman, Robin? Who could it possibly be? You and Bat-Girl have so much in common! You both fight crime in Gotham City in masks, red and green costumes and bare legs, alongside grown-ups dressed like giant bats. Is there really another girl out there more perfect for you than Bat-Girl? Who?
A statue, Robin? Really?
(Above panels from the story "Bat-Mite Meets Bat-Girl" in 1961's Batman #144, by Bill Finger, Sheldon Moldoff and Charles Paris)