Gadolhadorah: Perhaps you should ask why decorating the sucah or ANY other task not specifically mandated under Halacha is defined by gender? … Women can build a sucah…
Actually, it’s not so simple.
According to Rabbeinu Tam in Tosfos Gittin 45, a women cannot create a חפצא דמצוה which she is not commanded to perform. He talks specifically about Tzitzis, Sefer Torah, Mezuzah, Tefillin and Iggud of Lulav. The Rishonim extrapolate that according to the Rabbeinu Tam, she also cannot make a Sukkah. The Beis Yosef (OC”H 14) brings from the Mordechai הל’ קטנות אות תתקמ”ט that although the Sukkah she makes is כשר בדיעבד, she is not allowed to make a Sukkah (which is his position regarding Tefillin and Mezuzah etc.).
There is a Gemara (Sukka 8) which is mefurash that a woman’s Sukkah is Kosher; the Rishonim ask on the Rabbeinu Tam from this Gemara. There are various mehalchim to answer that Gemara – the Beis Yosef learns that it is only בדיעבד, but it is actually אסור. The Yaavetz (Mor UKetzia 14) learns that this is referring to a Sukkah built for women, not a Sukkah built by woman. See also Chasam Sofer Yo”d 271.