Do Catholics have a philosophical argument for why having more than one wife is wrong.
I am not interested in statements of faith.
God is not arbitrary: there is a rational basis behind all moral commandments.
Presumably, since the Catholic marriage is supposed to be symbolic of the relationship between Christ and the Church, there is some sort of notion that there is one Christ, one true Church, and therefore one man, one woman is the ideal of marriage.
Other than that, I can only think of practical considerations. Back in the day (and actually even now, in some parts of the world) when it was the responsibility of the husband to provide for his wife and children, it required (and still does require) a large amount of wealth to support more than one wife and the multiples of offspring that were likely to result from such a domestic arrangement. In fact, that is one of the main social arguments against polygamy - that those who are not wealthy are also denied the opportunity to marry and have children, whilst those men who have sufficient wealth accumulate more and more wives. That leads to large groups of young men who feel deprived and discontented with their lot.
I do appreciate the feminist critique of polygamy - it does, as it’s played out in a practical sense, treat women as little more than chattel. But if we expand this out to say that it’s likewise okay for a woman to have more than one husband, then this problem ceases to be. Although I suspect that if one were to propose to any group, such as some Mormons or Muslims, who actually practise polygamy, that if men have the right to have multiple wives, women should have the right to have multiple husbands, they would be either deeply offended or profoundly confused. So I suspect there is a solid foundation of sexism bound up in the idea of polygamy.
There is also a belief - one extending beyond the doctrines of Christian faith, I should say - that the love between one man and one woman is so sacred and so important and so…well,
romantic, that any interference with that is somehow sacreligious. That loving more than one person in the romantic/amorous/sexual sense is diluting the intensity of emotional attachment that is supposed to exist between a husband and wife. This is nonsense, of course, and leads to such absurd permutations as “serial monogamy” and people marrying and divorcing several times during the course of their lives, just because of the expectation that “one man and one woman” is the most desirable ideal.
So, in and of itself, I don’t think there’s necessarily a rational ground for supposing monogamy to be the only desirable, or even the most desirable, foundation for human families. There is an obviously sexist basis to polygamy as it has historically been practised, but if the concept is extended to polyandry, or even varying arrangements of men and women in loving intimate partnerships, that ceases to be an issue.