In the past Muslims used to answer the question that why woman cannot have more than one husband was that then we would not know who is the father of the child. But today we can find out who the father is by DNA testing. So today how can we answer the question why woman cannot have more than one husband?
The answer to that question was not merely because the child’s father could not be identified. Rather it is the natural order of the human condition. Having more than one husband per woman could destroy the social fabric in society and even cause moral decay. For the most part it is counter to our (i.e. men and women) nature to accept such a setup. Typically the nature of men does not allow them to share their brides and the competitiveness may render such a relationship impossible. This of course leads to the mention of the disparity between the populations of men versus women. Clearly in most societies women outnumber men and if such a condition were to be practiced the balance of the community would be in disarray. Thus it is the prohibition of nature that does not allow such a condition.
Consider another point regarding the model of polyandry. A child is born into a family yet the child’s identity is a mere guess until such tests are performed. Imagine the mutual trust and sense of attachment in a society, where the parenthood of a child is determined through biological testing. The bond may only develop after a positive ascertainment of who the father is. Not only can this create a flimsy foundation to the relational beginnings but it should be considered that such testing is not available world wide. Only a few countries have this available, thus compounding the problems with this type of family structure.
I hope I have clarified the issue.
God knows best.