I hate this quote. Rogers almost certainly never said it. She claimed that the first time she ever saw it was in this 1982 newspaper comic (by a man).

It was probably in circulation before that, but this comic strip (by a man) is probably what popularized it.
This stupid quote flies in the face of reality. The idea that Astaire had an easier time than Rogers is pure fantasy. In most of their movies together, Astaire had
at least one solo number,
many of them quite physically demanding.
Top Hat, White Tie, and Tails took 20 takes to get right because he kept breaking the cane toward the end. IIRC, Rogers only ever had
one solo number in all their movies together, Follow the Fleet, though I admit to not having seen all of them yet. Astaire also had
a solo routine in that same movie. A more accurate quote would be, "Ginger Rogers did about 80% of what Fred Astaire did, backwards and in high heels." But even that flies in the face of reality, because it minimizes their unique contributions.
Astaire worked on the choreography. Rogers helped with the wardrobes. Astaire famously hated the iconic dress from
Cheek to Cheek, but Rogers insisted on it. After seeing the daily, Astaire begrudgingly admitted that she was right to insist on it. Her choice of dress and stubborn insistence on using it were major contributions to what is arguably their most iconic scene together, as was the choreography by Astaire and Hermes Pan, as was Astaire's singing. They weren't doing the same thing, they were each doing different things that all contributed to the whole.
The idea that she always danced until her feet bled is greatly exaggerated. The most famous example, the first one anyone will point to, is the stairway scene from
The Last Dance in Swing Time. This took so many takes to get right that her feet were indeed bleeding by the end of it. When you see Rogers glide out the door at the end, she was heading straight for a chair they had waiting for her. Nobody forced her to do this, and in fact the producers suggested they stop filming for the night so she could rest. Rogers and Astaire
both insisted they keep going until they got it right. People tend to point to this as an example of her unique female suffering, but her suffering was intensified because she pushed past people trying to persuade her to minimize her suffering. Also, people exclusively focus on Rogers and her feet with respect to this scene, but do you suppose Astaire was ready to go run a marathon afterward? No one talks about him, but he was almost certainly dead on his feet, as well.
I can't speak for the ladies in this thread, but the people I've known IRL who love this quote really wish it were true that all women worked harder than all men at the same things for less recognition. They do this by minimizing the contributions of men like Fred Astaire.
That Fred Astaire guy? Pfff, he had it easy! He wasn't even wearing heels! Try being a woman! (I will not try being a woman, thank you.) This is as much a miscarriage of reality as overlooking Rogers' contributions or the unique difficulties of
doing this shit in heels. The reality is that men and women, like Astaire and Rogers, generally fill complementary roles. Rogers and Astaire complemented each other. They brought different things to the table and both made significant, different, contributions to the whole. I hate this quote because I think people should look at the Astaire-Rogers movies, and male-female relations in general, as a collaboration between complementary halves, not a zero-sum competition over who's got it harder.
I realize all of this is off topic, but this thread hasn't been on topic since page 1