The government should not have the authority to issue marriage licenses.

Polygamy has been one of the greatest oppressors of women in all of history, particularly when administered by fundamentalists religions. Pedophilia, selling child brides, and abuse are highly linked to polygamy. It's bad for men too, since only the wealthy have access to marriage.

Polygamy leads to certain partners being favoured over others, possibly causing conflicts between the parties and/or depression.