Why can Muslim men marry 4 wives and Muslim women marry only one husband?

In a nutshell: Islamic civilisation is based on large familial units, rather than individuals as is often seen in the West. Kinship ties and relations provide the functions we often see secular governments appropriating. As such, the larger the family, the more effective it is. The role of polygyny facilitates larger families whilst polyandry would do the reverse by limiting reproduction. Assumptions Considering this or any Islamic rule in isolation can be confusing. One has to remember Islam seeks to construct civilisations through the shariah, as opposed to providing a set of rules for individuals to follow in societies organised on secular principles. In the Islamic civilisation, society is comprised of a state (government) that is focused on primarily external affairs, and internal security and welfare, with kinship, based extended families expected to manage all of the affairs of their members. Families are therefore generally autonomous with husbands responsible for managing them, carrying significant delegated powers to get the job done. Hence the phrase often encountered in the West, the husband is the "Lord of the manor" - historically having had a similar role when Christianity was part of the ruling power structure. This allowed him to manage, organise and even discipline family members where necessary. In this context, larger families operate more effectively, with more children a greater asset to the productivity and welfare of the family.  This in turn also meant the central state was counterbalanced by large families in society coming together where necessary to limit its unnecessary interference or capacity for oppression should that ever happen. Polygamy, Polyandry and Polygyny Polygamy, or more specifically polygyny, in Islamic jurisprudence is permitted however not seen as mandatory. The foundational verse for permitting this comprises the following verse: وَإِنْ خِفْتُمْ أَلَّا تُقْسِطُوا فِي الْيَتَامَى فَانْكِحُوا مَا طَابَ لَكُمْ مِنَ النِّسَاءِ مَثْنَى وَثُلَاثَ وَرُبَاعَ فَإِنْ خِفْتُمْ أَلَّا تَعْدِلُوا فَوَاحِدَةً "And if you fear that you will not be just in dealing with the orphans, then marry of other women as may be agreeable to you, two, or three, or four; and if you fear you will not be able to do justice, then marry only one or that which your right hand possesses (concubines)." (Qur'an al-Nisa' 4:3) There are however conditions - the husband is expected to be fair and just towards each wife in marital affairs. If one cannot be fair or just, he is expected to restrict himself to one wife and his concubines. Perfect justice is impossible to achieve as mentioned in Sura al-Nisa' 4:129 so this is not expected from him. A wife can stipulate that she does not want him to practice polygyny and this can be grounds for divorce if he chooses otherwise. Legislative Goals (hikmah) Islamic scholarship elaborates five main goals 'al-kuliyaat al-khams' that Islamic legislation seeks to achieve. One of these five is the preservation of 'Nasl' or offspring and its continuity. The prophet (saw) encourages Muslims to marry and have large families contributing to a large ummah (community) when he said: تنَاكَحُوا تَنَاسَلُوا فَإِنِي مٌبَاهٍ بِكُمُ اَلأُمَمَ يَوْمَ اَلْقِيَامَةِ "Marry and beget children for I'll be proud of you before the nations on the Day of Resurrection." (al-Bayhaqi) Polygyny is the means to achieve this whilst polyandry seeks the opposite - which is why societies that practice polyandry reduce the reproduction rate and preserve limited resources.  Classical polyandry in Ladakh, an ethnic Tibetan region in India, has allowed families in areas of scarce farmable land to hold agricultural estates together. The marriage of all brothers in a family to the same wife allows plots of family-owned land to remain intact and undivided. In other cultures, such as some amongst the Inuit (formerly termed Eskimos), men may arrange a second husband (frequently a brother) for their wives as in their absence the second husband will protect his wife, thus his interests. If she is impregnated, it is by someone he approves. Given the vastness of the resources we have on the planet, and ultimately the universe, God encourages us to freely make use of them so there is no need for polyandry in relation to scarcity of resource. In terms of security, this is provided by the extended family, ranging from uncles to siblings to children, and ultimately the state. Again, polyandry is not necessary, polygyny fulfilling that process. The Quran thus cautions: وَلَا تَتَمَنَّوْا مَا فَضَّلَ اللَّهُ بِهِ بَعْضَكُمْ عَلَى بَعْضٍ لِلرِّجَالِ نَصِيبٌ مِمَّا اكْتَسَبُوا وَلِلنِّسَاءِ نَصِيبٌ مِمَّا اكْتَسَبْنَ  "And covet not that which Allah has made some of you excel over others. Men shall have a share of that which they have earned, and women shall have a share of that which they have earned." (Quran al-Nisa' 4:32) Lineage is then absolutely fundamental in Islam as it preserves the familial structures society is built upon - which is why so many Shari'ah rules are prescribed such as the nafaqah, inheritance, social kinship, marriage, and divorce. Even details, such as maintaining familial ties, are strongly emphasised: يٰۤـاَيُّهَا النَّاسُ اتَّقُوۡا رَبَّكُمُ الَّذِىۡ خَلَقَكُمۡ مِّنۡ نَّفۡسٍ وَّاحِدَةٍ وَّخَلَقَ مِنۡهَا زَوۡجَهَا وَبَثَّ مِنۡهُمَا رِجَالًا كَثِيۡرًا وَّنِسَآءً​ ۚ وَاتَّقُوا اللّٰهَ الَّذِىۡ تَسَآءَلُوۡنَ بِهٖ وَالۡاَرۡحَامَ​ ؕ اِنَّ اللّٰهَ كَانَ عَلَيۡكُمۡ رَقِيۡبًا‏ "And fear Allah through whose medium you ask one another and fear violation of ties of the womb" (Qur'an Nisa 4:1) "Whoever believes in Allah and the Last Day, let him maintain the bonds of kinship." (Sahih al-Bukhari) Penal rules relating to fornication/adultery (zina), often seen as very harsh and even barbaric, then make sense as warding off acts that may undermine this institution, create doubt, disputation and conflict in familial structures -  100 lashes for unmarried fornicators and the stoning to death of married adulterers. الزَّانِيَةُ وَالزَّانِي فَاجْلِدُوا كُلَّ وَاحِدٍ مِّنْهُمَا مِئَةَ جَلْدَةٍ وَلَا تَأْخُذْكُم بِهِمَا رَأْفَةٌ فِي دِينِ اللَّهِ إِن كُنتُمْ تُؤْمِنُونَ بِاللَّهِ وَالْيَوْمِ الْآخِرِ وَلْيَشْهَدْ عَذَابَهُمَا طَائِفَةٌ مِّنَ الْمُؤْمِنِينَ.  The fornicatress and the fornicator – flog each of them with a hundred stripes; and do not let pity for them hold you back from carrying out God's law, if you truly believe in God and the Last Day; and let a group of believers witness their punishment. (Qur'an 24:2) Therefore, Islam permits polygyny in order that large families can flourish. Polyandry in this context would seek to do the opposite. Conclusion The Islamic civilisation is based on large familial units, rather than individuals as is often seen in the West. Kinship ties and relations provide the functions we often see modern governments appropriating, the "paternalistic state", whether it be of welfare, education, work, financial or security. As such, the larger the family network (or tribe) the more effectively it can function and collectively with other networks counterbalance a central state, restricting its ability to become authoritarian or oppressive.  The role of a man in such networks is of governance, provide income and security; the wife's role is to support him in this and carry the responsibility of childbirth and rearing. Polygyny is permitted as it facilitates the development and growth of this social structure whilst polyandry is forbidden as it works against it by limiting reproduction. Both monogamy and polygyny are permitted forms of marriage in Islam whilst polyandry is prohibited as Islam envisions human society to comprise autonomous and prosperous familial units to flourish.