DY & KJ: If you read the Chasam Sofer inside, he does not bring “Kol Kevodah”. What he specifically says it is not the Kavod of Jewish Women “to go outside in public at the beginning of the night amongst men”. Logically, this is because there are groups of women (from the guild of Seamstresses) that do go out in the early evening amongst men, and no Jewish woman would want to be thought as one of those.
Once the “Minhag” became that women don’t light, it went forward from there even though the reason no longer exists.