“why can’t a woman read the megillah herself?”
It is pretty universally accepted that a woman can read the megillah for herself (see Shulchan Aruch Orach Chaim 689:1 — Magen Avraham objects but Mishnah Berurah supports the Shulchan Aruch) or for another woman. The machloket is whether a woman can read the megillah for a man.
“Where the Gemara and Shulchan Aruch says that women can read Megillah for men.”
Mishnah Megillah 3a, Gemara Arachin 19b. Rashi and Rambam hold that way. Shulchan Aruch Orach Chaim 689:7 brings a yesh omrim that a woman can’t read for a man (I think it is the BeHaG), implying that the accepted halachah is that she can. Mishnah Berurah sides with the yeah omrim. Rema says that she recites a different bracha than a man. Rabbi Ovadia Yosef paskens that a woman can read for a man. There are two rabbis in my own neighborhood who pasken on opposite sides of this one. CYLOR. (This is not Purim Torah but the real thing.)