So I'm now reading "Showcase Presents Supergirl, Volume Two", and if there's anything that a vast collection of black-and-white reprints of Silver Age comics has taught me, it's that the Superman titles are second only to the Wonder Woman titles in terms of sheer, wall-to-wall insanity. Case in point: The first meeting between Lex Luthor and Supergirl.
Luthor finds out about Supergirl's existence the same way everyone else does; Superman breaks into every TV show in the world for a special broadcast saying, "Hey, everyone! I've got a cousin!" (If I had a machine that let me interrupt every single TV signal in the world, I'd probably use it all the time to talk about my personal life, too. I'd be all, like, "Hey, world. Kinda had a sucky day at work. Could use some hugs." It'd be awesome.) On hearing about this, Luthor immediately suspects that this is a trick of some sort on Superman's part. He breaks out of prison (fun science fact! Combining mouthwash, aspirin, orange juice, and some old radio parts will make a fool-proof invisibility formula that works whenever a siren goes off!) and goes to defeat what he assumes is a robot Supergirl.
Of course, she's not a robot (not that this would be out of the question in a Superman title; she actually has robot impersonators of her own) and Luthor realizes that she is, in fact, a woman with all of Superman's powers. He remains confident, though; Luthor says, "I'll use her feminine nature against her!" He pulls a bank robbery, using a shrinking beam to steal the entire bank (hey, Silver Age Luthor might have been crazy, but he had style!) and sets up a trap for when Supergirl shows up...one that will use her "feminine nature" against her.
Specifically, he has an accomplice waiting with a baby carriage, and when Supergirl shows up, they shove it down a hill and tell Supergirl that she's got enough time to save the baby or stop Luthor, but not both. As it turns out, the baby carriage actually has a midget with Kryptonite in it, but that's not the point. (As difficult as it is to avoid puzzling over, it's really not.) The point is, Luthor apparently believes that the big difference between a man with Superman's powers and a woman with Supergirl's powers, the "feminine nature" he's using against her, is that Supergirl will let Luthor escape to focus on rescuing the baby.
The clear implication is that Superman wouldn't. "Screw the helpless infant, Luthor! You've got a date with the judge!" That's right, Luthor clearly knew that only female super-heroes care about children's lives! Or just that Superman is a dick.
Anyhow, Supergirl escapes from the midget and actually saves Luthor's life in the process of capturing him (mainly, according to her, because Luthor's got a life sentence in prison to serve, and she's not going to let him get out of it by dying young. Which is actually a pretty impressively badass thing to do. It sort of feels like what Judge Dredd might do to a perp who's doing life.) Afterwards, Luthor resents her bitterly for saving him, thus cementing her position in the Superman family. And cementing this story's position in the canon of crazy Silver Age stories.