Michael, is there any real reason to maintain the conflation that a male person ends a swing on the left and a female person ends a swing on the right? I see none.
Nobody is proposing "funny terms for people when [...] we already have perfectly good terms". There aren't any terms for people. Just those dang terms for dance positions that happen to have historical conflation with genitalia.
Far too many new (and even not-so-new) dancers of whom I've asked "do you have a preferred role for this dance?" have never even considered the possibility that role has absolutely nothing to do with one's gender. They have never considered dancing the "non-traditional" role because of the subtle (and sometimes, regrettably, overt) reinforcement of the male-dancer="gent"-position female-dancer="lady"-position.
Why reinforce that conflation at all?