A - Thanks for the question. In our modern culture, marriage is being constantly redefined. Not long ago, it was the cultural norm that marriage was between one man and one woman, till death do they part. Now, marriage is whatever someone can think up - same-sex marriage, polyamory, polygamy, etc.
We must first understand what the Church teaches about marriage before I get into polygamy.
WHAT MARRIAGE IS
Marriage is the basic cultural building block of society. One man, one woman, and their children unite as a family - every bit of evidence shows that families thrive in monogamous and stable homes with two biological parents of opposite sexes who remain married.
This means that there is less poverty, crime, strife, etc. in homes where marriages do well. This is because the mother and father of children cannot be replaced. Two fathers or two mothers (or any other combination of differing numbers) cannot provide what one mother and one father can. The role of the father can't be replaced by a woman and the role of the mother can't be replaced by a man. Neither can multiple mothers help a confuse child understand why daddy has many wives.
When families suffer the rest of our culture suffers.
NOT ABOUT "LOVE"
True love is to choose what is best for the other regardless of the cost to myself. This means polygamous relationships can never have loving sexual relationships. This is because the true act of sex is about giving yourself away, but if a man has multiple wives he can't do this fully with one woman, because the body isn't made to be given to multiple partners and it certainly doesn't proclaim faithfulness to one other person.
A married couple can say, with their bodies, I want to create life and bond with you only - for life. I want to be one with you. This is impossible with polygamous "marriages", because while the body might still be saying this, the act itself is ordered toward selfish pleasure.
NOT ABOUT EQUALITY.
Marriage laws are by definition discriminatory. They discriminate FOR traditional families (not against others) in order to build up what is good for society. Where do children thrive? In the traditional family. If we tear that down, then society will suffer. Thus, the government needs to help support this building up of what is good for society. Therefore, marriage is about more than people who have good feelings for one another. It is about the good of society - which is why the government got involved in it in the first place.
WHAT ABOUT OLD TESTAMENT POLYGAMY?
In the times of the Old Testament, the people were being led by God toward the truth, but He didn't give them the fullness of the truth, because they were not ready for it. If the Father had sent the Son during the times of Noah, the people would not have been prepared to accept Him. Therefore, we can see the Old Testament as a school for humanity. It is a training and education in the basics so that we would be ready to accept the advance education and training of Christ. When Jesus came, He revealed the fullness of the law of God. So, the moral law - the 10 commandments - was never taken away. Rather, our understanding of it was deepened (see Matthew 5-7).
What was changed were those things that were not part of the moral law. For instance - Christ says this about divorce and why God allowed it in the Old Covenants:
"Some Pharisees approached him, and tested him, saying, "Is it lawful for a man to divorce his wife for any cause whatever?" He said in reply, "Have you not read that from the beginning the Creator 'made them male and female' and said, 'For this reason a man shall leave his father and mother and be joined to his wife, and the two shall become one flesh'? So they are no longer two, but one flesh. Therefore, what God has joined together, no human being must separate." They said to him, "Then why did Moses command that the man give the woman a bill of divorce and dismiss (her)?" He said to them, "Because of the hardness of your hearts Moses allowed you to divorce your wives, but from the beginning it was not so. I say to you, whoever divorces his wife (unless the marriage is unlawful) and marries another commits adultery." [His] disciples said to him, "If that is the case of a man with his wife, it is better not to marry." He answered, "Not all can accept [this] word, but only those to whom that is granted. Some are incapable of marriage because they were born so; some, because they were made so by others; some, because they have renounced marriage for the sake of the kingdom of heaven. Whoever can accept this ought to accept it." - Matt 19:4-12His answer to the question of why divorce is allowed gives us insight into the training that God was giving His people. But, God wants more of us. He wants us to live life out fully and with all truth, therefore He gave us the grace to be able to do so through Christ - both in His teachings and in each of our souls. The same kind of situation happened when the law allowed for multiple wives.
The Bible doesn't answer the question of polygamy directly, but we can infer much from this situation. This was because the tribes and kingdoms which surrounded Israel allowed for the same, and the Israelites were not ready to accept the fullness of the law. Therefore men were allowed, for a time, to have multiple wives. Why?
Well, maybe because there are more women than men (due to war, lifestyles, etc. of ancient times). Also, an ancient near middle-eastern woman would not be able to provide for herself and would need the support of a relative or husband. In the new covenant of love that Christ reveals to us, we see that marriage is to be between only one man and one woman, because this relationship mirrors the relationship between Jesus and the Church (Ephesians 5) and that the two become one. The new law is one of love and faith, not just rules.
"I give you a new commandment: love one another. As I have loved you, so you also should love one another. This is how all will know that you are my disciples, if you have love for one another." -John 13:34-35Finally, the Catechism says the following:
2387 The predicament of a man who, desiring to convert to the Gospel, is obliged to repudiate one or more wives with whom he has shared years of conjugal life, is understandable. However polygamy is not in accord with the moral law." [Conjugal] communion is radically contradicted by polygamy; this, in fact, directly negates the plan of God which was revealed from the beginning, because it is contrary to the equal personal dignity of men and women who in matrimony give themselves with a love that is total and therefore unique and exclusive." The Christian who has previously lived in polygamy has a grave duty in justice to honor the obligations contracted in regard to his former wives and his children.Ultimately, the answer lies in this fact - we were made for one other person. That relationship will ultimately be with God in heaven, but in this present life, we are made to be a sign (Sacrament) of that relationship with God in our marriages between one man and one woman, until death.
I hope this helps.