A BIT OF BACKGROUND
I know that in Jewish law there are some ritual requirements, positive duties caused by time, which obligate men but not women. The gemara mentions this idea both in the context of consistent examples and in the context of exceptions, ritual requirement which do obligate women, such as kiddush on Shabbos. For a few examples see Kiddushin 29a, Kiddushin 33b, Berachos 20b, Shabbos 23a, Pesachim 108b, Succah 28a, Rosh Hashanah 33a, Succah 38a, Kiddushin 34a, Arachin 3.
But in general, there is a presumption of equal rights (Bava Kamma 15a, citing Num 5:6, Ex 21:1, Ex 21:29), and prohibitions usually apply to men and women equally.
THE REAL QUESTION
So why are women permitted to cut their payot (sideburns)? The commandment involved there is not a positive time-bound commandment; it's a prohibition!
I don't mean to ask philosophically why God made it that way (like "Taamei HaMitzvot"). I'm asking what is the Derasha or verse that Talmud (etc.) uses to derive it.