In Jane Austen's Emma, the heroine is at a ball with her brother-in-law, when the following dialogue occurs:
“Whom are you going to dance with?” asked Mr. Knightley.
She hesitated a moment, and then replied, “With you, if you will ask me.”
“Will you?” said he, offering his hand.
“Indeed I will. You have shown that you can dance, and you know we are not really so much brother and sister as to make it at all improper.”
“Brother and sister! no, indeed.”
My question is - what would be seen as "improper" about a brother and sister dancing together at a ball?
I know that dances were seen as a chance for courtship, but certainly not exclusively so - there are references to married men dancing with other women or women dancing together, so dancing was clearly not seen as inherently sexually charged. And in any case, it seems unlikely that Emma would actually be referring to incest. So what is improper about it?
Emma is based in the early 19th Century, and during this time period going to the ball was one (if not the only) way for young men and women to meet. Ultimately, the whole purpose for a young man or woman to go to a ball was for courtship. Dancing with someone you like, was seen as a act of courtship, and was also the appropriate way to physically come close to the other person.
So that is why it would've been seen as improper for siblings to dance together, even it wasn't in the act of courtship. To those who would be watching, parents, and other notable figures of society, it would've been seen as improper.
This is a great read for different situations about dancing during Jane Austen's time period, with references to her: https://www.google.com/amp/s/austenette.wordpress.com/2008/09/20/ballroom-etiquette/amp/
They also echo, at the end of their article what I have been taking about and it appears to apply for all situations regardless how casual it was: "brothers and sisters weren’t allowed to dance together."
Emma is also classified under the "book of manners" genre. Where the author recreates society, observing customs, social norms, values etc. What she is writing is a reflection of what society was like during her time.