There are many reasons for this actually.
When humans started to form societies, and even before that in tribes, it was important to know who the next "king/leader" will be which was setup through patriarchal lineage generally speaking. In addition to this societies that were not monogomous would be more unstable due to jealousy and other basic human emotions. Even today in our "advanced" society it's very difficult to maintain an open relationship due to these emotions. That instability leads to a weaker society and nation, which means they are more likely to fail through their society collapsing or being conquered by stronger societies. Add in the Church and other religious institutions where monogamy was stressed as very important.
Looking at societies where they didn't practice monogamy, you see a large amount of them being based on polygamy (i.e. one many, many wives). This is problematic for many reasons. First off it creates an environment where women are treated more as property and not afforded the same rights as the men. Secondly, it creates a society where extremely young women are basically "forced" into a marriage with an old man (i.e. age 13-14) regardless of their wants/desires/choices. Finally it leads to a weakening of the gene pool, and one where weaker and less attractive men get no women at all while the rich and attractive get all of them. With modern views on equality and what human rights are and should be, it's pretty hard to have a functioning polygamist society.
Polyamory (i.e. one person multiple partners, where men and women both have more than one spouse) however has a strong following out there and it's growing. The GLBT movement and the free love movement both have helped to advance polyamory into being viable. Even thought it is now a possibility for people to have a functioning poly lifestyle, it's not easy for many to live with. Those basic human emotions like jealousy and such still rear up every so often. It's goes against societies generally accepted lifestyle of monogamy being the only "right" way to live which creates stress that can break a relationship (many families won't accept it, a lot of friends won't like it, and it will alienate people).