Hi, I have heard that woman should light menorah candles i.e girls even in their parent’s homes. What is the source not to?
Women have to light Chanukah candles just like men, because they we also part of the ness, however it seems that the custom was that only the husbands lit candles and includes the wife in her obligation, and that the wives or girls don’t light on their own. Nowadays there are many girls that do light. Without getting into the actual question if they should or shouldn’t. Your question was, what are the sources that they don’t, here are some of the sources. .
The Mishnah Berura 671-9 says that married women don’t light because they are one with their husbands. Regarding single girls, the sources for the minhag that they don’t light is the Olas Shmuel siman 105 brought in the Mishna Berurah 675-9, that women are included in the men’s lighting. There is also the Chasam Sofer Shabbos 21b that since the original mitzvah was to light outside and since “kol kovod bas melech pinima” therefore women don’t light actually light rather they are yotza with the men ( if there is a man that may include her in his lighting). Also see Teshuvos Vhanhagos 2-342 (7) that suggests another reason.