The reasoning behind the prerequisite, according to officials, is that spaceflight could potentially harm the women's fertility.
How can space travel affect a woman’s fertility?
The most obvious issue is exposure to radiation. Once you're beyond the earth's atmosphere and magnetic field you are exposed to much higher levels of radiation from cosmic rays and solar flares. It's also possible that microgravity (weightlessness) could have effects on the reproductive system, but this isn't well studied yet.
However, given the source you link to to (a nine year old article speculating on why China required female astronaut candidates to be wives and mothers), this may simply be a medical rationalization for a political decision. Radiation can damage male fertility too, and the effect of microgravity on the male reproductive system is also not well understood.