The gemara (M.K. 14b) writes that there is no aveilus on Yom Tov because the mitzvas aseh d’rabim of simchas Yom Tov is doche the individual’s obligation to mourn.
The Rambam paskens (Chagigah 1:2) that both men and women are obligated in the mitzvah of simcha. Ra’avad, however, disagrees. The gemara asks how women could be obligated in the mitzvah of simcha, which is zman gerama, and the gemara answers that “isha ba’alah m’samcha.” Tosfos explains that the gemara means that there is no chiyuv on women to bring shalmei simcha – there is just a chiyuv on their husband to share their korban with them (see Rashi). Kesef Mishneh says that the Rambam in fact agrees with this view; when the Rambam says women are obligated in simcha he means they eat from the korban brought by their husbands, not that they must bring their own korban. The Rambam just did not go into the details.
If women have no independent obligation of simcha, asks the Minchas Chinuch, then why are they not obligated in aveilus on Yom Tov? They have no aseh that is doche their mourning!
Rav Neventzal (quoted in the footnote to his sicha for Parshas Behar) suggests a brilliant answer to this question. The Rambam writes (Chagigah 2:14) that shalmei simcha should be shared with the poor and needy, as a person has a responsibility to see that others have simchas Yom Tov as well. By “aseh d’rabbim” the gemara does not mean an aseh that a lot of people are obligated in – what the gemara means is that my simcha is dependent on others, on the community, being happy as well.
Were a woman to observe aveilus on Yom Tov, even though she might not have any independent chiyuv of simcha, her being in aveilus would conflict with my personal chiyuv of simcha. So long as someone in the community is unable to be b’simcha, something is lacking in my kiyum mitzvah as well.
This is a two for one deal: not only is it a tremendous lomdus, it’s a tremendous mussar as well. A person should not feel shaleim and b'simcha while others are in need.
I would like to suggest another possible answer based on an idea the Rav suggested in Shiurim l’Zecher Aba Mari. RYBS distinguished between the ma’aseh mitzvah of simcha, which entails eating korbanos (or eating meat and drinking wine b’zman ha’zeh), and the kiyum mitzvah, which is a kiyum b’lev of being happy. There is nothing that stops an aveil from having a meal of meat and wine – why does the gemara see a conflict between the mitzvah of simcha and the chiyuv aveilus? Because the gemara understood that the meat and the wine are just a means to and end; it’s the emotional state that they engender which conflicts with and undermines aveilus. Perhaps the Ra’avad’s disagreement regarding the chiyuv of women in simcha is only viz a viz the kiyum b’poel of offering korbanos or other specific actions. However, with respect to the idea of being emotionally b’simcha on Yom Tov, the Ra’avad would agree that both men and women are equally obligated and therefore aveilus is disrupted.
Why do I think there is no ptur of zman gerama for the mitzvah of simcha which is a kiyum b’lev? A few ideas:
1) The Avudraham explains that women are exempt from zman gerama mitzvos because they are busy running a house and therefore the Torah placed fewer obligations upon them. That reason works for mitzvos b’poel, but does not seem to apply to what emotional state one should be in.
2) Before Pesach we discussed a yesod from R’ Leizer Silver that there is no ptur of zman gerama by mitzvos sichliyos. Perhaps the obligation to be happy on a holiday is something intuitive (what is a holiday all about if not being happy?) and therefore women are obligated.
3) Perhaps this secondary mitzvah of simcha (beyond the obligation to b’poel eat korbanos) is only derabannan (see Tos M”K 14b) and the Ra’avad holds that there is no ptur of zman gerama by derabbanans (see post here).