Christianity did not have to argue its way to monogamy from scratch, because Roman law already recognised one wife at a time, and the earliest churches grew inside that legal culture. What Christianity added was a reason. The gospels have Jesus citing the passage in Genesis about a man leaving his parents and the two becoming one flesh, and the letters develop a comparison between marriage and the union of Christ with the church. A union of that shape cannot be divided between several partners without losing the thing it is being compared to.
The pastoral letters require an overseer to be the husband of one wife, a phrase that has been read for two thousand years as excluding polygamy, or remarriage after widowhood, or serial divorce, depending on who is reading. The medieval West then made marriage a sacrament and indissoluble, and the Council of Trent fixed that position against the Reformation, which had reopened the question of divorce but not of plurality.
The rule travelled with the missions and met societies where plural marriage was ordinary. That produced a practical problem the churches have never resolved cleanly: a man with four wives who wishes to be baptised is asked to dismiss three, and the women dismissed lose their standing and their support. African churches, including African Initiated Churches, have taken a range of positions on this, and it remains a live pastoral question rather than a settled one.