I think the problem with polygamy from a Christian perspective is in the equality of men and women that comes through Christ. “In Christ there is neither Jew nor Greek, Slave nor Free, Male nor Female.” No racism, No classism, No sexism. Jesus came to bring about a new covenant in His blood. It moved from a law based, oppressive religion, to one that liberates. Its hard for us to wrap our minds around it because we are so inclined toward patriarchy. I would even say that Paul tends to be instinctively patriarchal, but battles with it through his letters. Paul writes his letters to churches being formed in patriarchal communities, to people who have only functioned in patriarchy - for them and for us, it is difficult to get beyond the oppression of patriarchy. Jesus does not favor men over women. Jesus was beyond patriarchy - He considered women to be valuable in a way that no other men seemed to - Jesus taught women and clearly in the early church, women were hungry to learn and through the teachings of Christ they were given a freedom they had never had before.
With this in mind, as far as Jesus is concerned, women and men are not far different from each other and may be different, but seem to be equal.
That said, If a man wants to have more than one wife, he must also accept a woman who wants to have more than one husband.
Personally, I’m not comfortable with that idea. I don’t want to share my wife with another man. I don’t think its just socially built into my thinking - I don’t think of that as appealing, the idea of sharing my wife as a sexual partner with another man… that just seems vile… buh!!
I personally think that God wants us to be monogamous. As we imitate Christ (who is loyal to his church - the only way to God) we should be loyal to only one spouse.
As far as what Jesus says about marriage, he only talks about monogamy, seemingly dismissing any need to discuss polygamy, as though it isn’t even an option.