Question: My question is: 'Why can men have four wives and women just one husband?'

Answer: I'll first address the issue of men having four wives before I answer your question as to why women can't have multiple husbands. 
    I think that among many other misconceptions about Islam is the notion that it unconditionally allows a Muslim to have four wives. In this regard, some scholars have gone as far as to say that keeping four wives is a man's essential physiological and psychological need. I am afraid that this point of view is in direct contradiction with the Qur'an. It is, in fact, a distortion of the stance of Islam. According to the Qur'an, in normal circumstances, a family comes into being only through wedlock between a single pair of man and woman. A subtle reference to this is made by the Qur'an (4:1) where it alludes to the fact that when the Almighty created Adam, he made Eve for him as his only wife. Naturally, had the Almighty intended that a man should have more than one wife, he would have created more wives for Adam instead of just one. This shows us that as far as a man's physiological and psychological needs are concerned, they are completely satisfied even if he has a single wife. 
    Let us now take a look at the verses which are generally thought to be the basis of polygamy. But first a brief word about their background. A greater part of Surah Nisa, in which these verses occurs, deals with the society and its reformation. In this regard, the foremost sphere in which directives were given was that of the welfare of the orphans - since they are one of the weakest sections of society. In Madinah, there came a time when many Muslims were martyred in various battles. As a result, many children were orphaned. In this situation, an appeal was made by the Almighty to the Muslims. They were urged to look after these children and guard their wealth and property. In this regard, the already in-practice custom of polygamy in the Arabian society was resorted to. Muslims were told that if they were afraid that they would not be able to take proper care of these orphans, they should marry their widowed mothers. 
    We will now take a look at the actual verses:

If you fear that you would not be able to deal justly with the orphans, marry two, three or four of the women who are lawful for you. But if you fear that you would not be able to deal justly [with them] then [restrict yourself to] one only. (4:3)

    Three implications of this verse are very clear:
    Firstly, polygamy is related to some social need. 
    Secondly, the number of wives should not exceed four in any circumstances. 
    Thirdly, if a person cannot maintain balance and do justice to his wives, he must restrict himself to one. 
    In other words, while in normal circumstances, a family comes into being through the union of a single man and woman, there may be certain exceptional circumstances in which the practice of polygamy many be benefited from with the restrictions mentioned in the above quoted verse. For example, in our society, many young widows and divorced women with small children have to live a life of misery and no one is willing to accept them as wives. Such widows and children can lead normal lives if this permission is benefited from. Similarly, many young women converts who have been abandoned by their non-Muslim husbands need Muslim husbands. So, a number of problems can be solved by using this permission, which would have been impossible to overcome had Islam totally forbidden polygamy.
    With this background, I'll now come to your question regarding polyandry (woman having many husbands at the same time). It is common sense that if a family is to come into being not only should there be only one head but also one person should not be placed under the command of multiple heads other wise, great anarchy would result. Since, in the family set up envisaged by Islam, husbands are to head the family, if a wife has multiple husbands, she would be placed under the authority of many husbands at the same time. This of course would only hasten to tear apart the fabric of a family unit. Furthermore, the lineage of the child borne by a woman having more than one husband cannot be ascertained. How would the father be ascertained? Someone might say that a DNA test would be able to do so. However, even if this test is used, there still are great chances of dissent between all the husbands with one claiming to be the father and the other denying him.
    Owing to these reasons Islam has not allowed women to be married simultaneously to multiple husbands.