Just google “Rabbi Gershom ben Judah” for the explaination. His writing are the most clear on the subject.
In EXTREME brief, there are numerous statements in the Torah that polygamy was a bad idea, available in special circumstances only, and numerous examples of the trouble it caused in general, from murder to inter-sibling jealousy, rape, and sibling murder.
Contrary to popular belief, polygamy is never “sanctioned,” merely tolerated (under specific circumstances), even under strict Karaite reading of the Torah.
In the Mosaic Law if you were married, but your brother died and his wife had no offspring yet, you were comanded to marry your sister in law and bring forth children in your brother’s name. Also, if you were married, and you were caught cheating with an unmarried woman, you had to take her as an additional wife and you were not allowed to divorce her.
From my understanding, Jews teach that the 10 Commandments forbid a man from coveting another man’s wife but that an unmarried woman can covet a married man because she has the possibility of marrying him.
In all these cases one has to admit that God endorsed polygamy. Also, when Nathan condemned David for sending a man to his death so he could gain his wife he told David that God (yes, God) had blessed David with 6 wives but that David had done wrong in stealing another man’s wife and causing him harm.