Gawain never went to his school dances, when he was alive.
His parents thought proms and socials were wastes of time that could be used for studying, so while his classmates were out dancing and having fun for these school functions, Gawain was at home, doing extra credit work. Or pretending to do extra credit work while his parents were looking and playing with Arthur when they weren’t.
Even after he died, he never had much reason to dance. He was spending almost 100% of his time invisible and intangible, and trying to help his now-grown brother cope with the loss of his arm and his best friend. Dancing was something that just...never came up.
It was never an issue once he became a superhero, either, and the few times it was, Gawain could always back out of it by claiming to be afraid of ‘stepping on his partner’s toes’ (a fair concern for a robot, really). But then Batman needed League members to attend a charity function (hosted by Bruce Wayne of course), and it came to light that Gawain never danced because he didn’t know a waltz from a tango.
Green Lantern and Superman both turned out to be useless dance teachers, and Diana, as it turned out, didn’t know how to waltz either. Hawkgirl didn’t ‘do’ dancing, and Flash’s idea of dancing involved trend names like ‘Funky Chicken’. That left only one person Batman could trust to teach Gawain how to properly dance in time for the function.
Gawain was sworn to secrecy once the lessons concluded.