Does anyone know why the Zavah (a woman who experiences certain menstrual bleeding outside her regular cycle) brings a sin offering on the eighth day after the bleeding ceases? (Leviticus 15:29).
Although the question originally conflated a zavah with woman who is niddah, this obligation applies to a woman who is experiencing discharge beyond her regular menstrual cycle. Regarding the offering brought by a Zav, the male counterpart of a Zavah, the Ibn Ezra on Lev. 15:15 explains that an offering is brought because such discharges are divine punishment for sin. The Ramban adds that the offering expiates the sin to avoid recurrence.
A nidda doesn't even have an 8th day - Min Hatorah she goes to the mikvah on the night after the bleeding stops. The 7 clean days is only for a Zavah.
In modern times we (theoretically) don't know who is a Niddah vs a Zavah so both wait, this change was instituted by women BTW.
I say theoretically because we still do it even in cases where it's obviously Niddah and not Zavah.
Zavah is bleeding outside the expected time. In questionable situations the Sanhedrin was consulted, and we don't have that now.
We could in theory act like a Zavah in all questionable situations, but we don't. We act like Zavah in all cases, this was the change instituted by women.