Question: Why is homosexuality an abomination, but Deuteronomy 21:15 talks about polygamy as though it is a perfectly accepted practice.
Answer: Deuteronomy 21:15 reads, “If a man has two wives, the one loved and the other unloved, and both the loved and the unloved have borne him children, and if the firstborn son belongs to the unloved…” This verse seems to give a tacit approval to polygamy. Let me answer the question in two parts. I believe homosexuality is disapproved (especially in light of Romans 1) because it is a reversal of God’s created order.
Regarding polygamy, I am copying Hank Hanegraaff’s answer for you. It is from his website, equip.org:
“Haven’t you read,” he replied, “that at the beginning the Creator ‘made them male and female,’ and said, ‘For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh?’ So they are no longer two, but one” (Matt. 19:4–6).2
Polygamy, the practice of one man having multiple wives, was common in antiquity. Though practiced in the Old Testament, polygamy was never God’s perfect plan.
First, the ideal pattern of monogamous marriage of one woman and one man was established early in Genesis: “For this reason a man will leave his father and mother and be united to his wife, and they will become one flesh” (2:24). Moreover, this very passage was quoted by both Jesus and Paul in defense of the sacredness and exclusivity of monogamous marriage (Matt. 19:3–9; 1 Cor. 6:15–17; cf.1 Cor. 7:2).
Furthermore, the Bible explicitly condemns the polygamy of Old Testament kings (Deut. 17:17). Likewise, New Testament elders and deacons are called to be “the husband of but one wife” (1 Tim. 3:2, 12; Titus 1:6). Just as the requirements for church leaders set the standards of morality and spiritual maturity for all believers, so too the admonition against polygamy for the kings of Israel demonstrates the danger of this practice for all.
Finally, God’s disdain for polygamy is seen in its consequences. The Old Testament clearly reveals the familial strife and temptations that accompany the practice. Solomon is the quintessential example of one whose legacy of faithfulness was compromised because of his polygamous behavior. Despite his world-renowned wisdom, Solomon’s peaceful and prosperous rule ended in idolatrous scandal and civil strife, for “his wives turned his heart after other gods” (1 Kings 11:4).
For further study, see Gleason Archer, Encyclopedia of Bible Difficulties (Grand Rapids: Zondervan, 1982).
— Hank Hanegraaff