Praise be to Allah.
With regard to why Islam does not allow a woman to marry more than one man, the imams (may Allaah have mercy on them) have explained the wisdom of the Lord behind that. For example, Ibn al-Qayyim (may Allaah have mercy on him) said:
That is the wisdom of the Lord and His kindness and mercy towards His slaves and His taking care of their affairs. Exalted be He far above anything other than that. His laws are above suggesting anything other than that. If it were permitted for a woman to have two husbands or more, the world would be corrupted, lineages would be lost, the husbands would kill one another, there would be great misery and tribulation, and there would be continuous trouble.
How could a woman be in a good position if she were shared by a number of men who were fighting all the time? How could the men who share her be in a good situation?
The fact that sharee’ah brings the teachings it does is one of the greatest signs of the wisdom of the Lawgiver and His mercy and care.
If it is said, how come men are taken care of and given free rein to satisfy their desires and move from one wife to another according to their desires and needs, when a woman’s sex drive is the same as a man’s?
The answer is that because women are usually hidden behind veils and inside their houses, and women tend to be more even-tempered than men, and less active than men, and men have been given more physical strength and energy which makes men’s desires greater than woman’s and men are affected by these desires more than women, a man is allowed to marry more partners than a woman is. This is one of the things that have been given exclusively to men and not to women, one of the things in which they have been given something more than women, just as they are also favoured over women in that only men can be Messengers, Prophets, caliphs, kings, governors and judges, and go out for jihad, etc., and men have been made qawwaamoon (protectors and maintainers) of women, taking care of them, working to provide them with the means of living, exposing themselves to danger, travelling about in the land and exposing themselves to all sorts of trials in order to take care of their wives.
The Lord is Ever-Appreciative and Forbearing, so He appreciates the men's efforts and has rewarded them by giving them something that He has not given to the women.
If you compare the exhaustive efforts and hard work that men do for the sake of woman with the jealousy that women suffer, you will find that the men's share of effort and exhaustion is greater than the women’s share of having to put up with jealousy.
This is the perfect justice, wisdom and mercy of Allaah, may He be praised as He deserves.
See also Question No. 10009.