Why is it not permissible for a woman to be married to four men at the same time as it is permissible for man?

One of the extremely important points that is often neglected by modern society is the right that Islam has granted women but not to men. Man can only marry unmarried women, whereas a woman can either marry a single or a married man and this is meant to guarantee the attribution of children to their real father and to protect the children's rights and their inheritance from their father. Islam allows a woman to be married to a married man provided that he has less than four wives and can fulfill the conditions of justice and ability. Thus, a woman is allowed a wider range of choices from among men and has the opportunity to learn how to deal with the co-wife and how to approach marriage while being aware of the morals of this husband.

Even if we assume the possibility of maintaining the children's right through the DNA test owing to the scientific advancement, what is the mistake of the children to deserve being introduced to their father through such a test? How would this affect their mental state? Moreover, how could one woman manage to be a wife to four men with such moodiness of hers?! All this along with the diseases that she could get as a result of her intimate relation with more than one man at the same time.