Salaam all.
I just joined to clarify a few things about polygamy
'Marry woman of your choice in twos' threes' or fours' but if ye fear that ye shall not be able to deal justly, (with them), then only one' [Al-Qur'an 4:3]
'It is very difficult to be just and fair between women'. [Al-Qur'an (4:129)]
There are many reasons. Firstly, there is no relation outside marriage. This is self explanatory.
Secondly, it gives women a chance. The Prophet Muhammad only married widows except Aisha. Every country (aside from China and India due to abortion) has many more (millions more) women than men. Say, for example, all these men were married to one woman each. Where will the other women go? Will they become second wives and receive equal rights, or will they become 'mistresses' and break families apart, as well as not receiving true dignity?
Alright, that's that. Now, why cannot women marry more than one husband? This ties with the logic of above. In Islam, it is compulsory that a man spends his wealth on his family, while a woman does not have to share it (this is also the primary reason why men get more in inheritance). And now comes the common sense bit: If there are more women then men on earth, what of 'supply and demand'?
And last of all- what if there is a war? Many men die, and the women are left alone. Can they not marry another man? Is that not fair? There was a great number of unmarried/widowed women after WW1 and WW2. There are similar scenarios where this happens.
The main point is that adultery, cheating, etc is not allowed in Islam, and it breaks up families, regardless of religion. Almost all main religions allowed polygamy (Yes, even hinduism) until the polygamy law was ruled out in the last century. IMO, it was a bad move.