Now it has to be said, Silver Age Supergirl is a terrible flirt. In fact it's Supergirl standard plot trope #2: Supergirl falls for someone inappropriate and it all goes horribly wrong. Consequently, it's hardly surprising that she'd occasionally fling herself at a guy who was actually a girl in disguise.
No, I lie. That's still weird. But it is all very Shakespearian. Except, despite all the cross dressing, Shakespearian couples invariable end up as male/female.
So in Adventure #384 Linda is jealous of her friends of the issue, who have been computer dating. She's sad that she can't use the service to get a proper match because she couldn't give her true details, and anyway, no Earth boy would be up to her standards.
Superman's advanced high tech computer concludes that Supergirl would be best matched with Volar of the planet Tomar. Why it picks this person requires some speculation. I'm guessing that either 1) Superman, at his most passive aggressive fixed the results, b) the computer knows more about Supergirl than she's admitted to herself, or iii) it's a piece of junk.
Superman really is a dick sometimes.
Supergirl flies to Tomar for the weekend, and immediately finds Volar. He invites her home to meet his parents, which is maybe moving a little fast, but she's keen. Meeting Volar's father, she notices that his mother is treated as a servant. Tomar explains that women are considered inferior on his planet. It's been this way for centuries, since some galactic
The two continue about their superheroing business, catching crooks and rescuing people, but Supergirl finds herself mocked and belittled because she's female. Whether this is the first time Supergirl has faced prejudice, I don't know, but she doesn't like it.
But then she's also put out that Volar is failing to, um, put out, complaining that after several hours in her company he hasn't yet tried to kiss her or even hold her hand.
Later that day, while spying on Volar having a quiet chat with his father, Supergirl learns that Volar will have to give up his career as a superhero the very next day, as they've run out of a mysterious serum and can't make any more. His father tells Volar to get rid of Supergirl, so she won't see what happens.
She hangs about all night, and when they see she's still there in the morning they invite her in. The shock sends Supergirl fleeing back to Earth "where I belong!"
Supergirl comes off as spectacularly self-centred here. She's embarrassed by her own behaviour, and can't see beyond that to the plight of her colleague, so ground down by prejudice that she has to save the world dressed as a guy or she won't get any respect, or the society which has cast their entire female population into virtual slavery on the word of some visitor who, by his own admission, was out to get back at all women because he got dumped. But then, as is clearly indicated, Superman knew about the entire situation beforehand, and he was entirely okay with it.