(Got the excellent write-up below from a well researched website):

Question

‘[Your literature] often says that Genesis shows that “God intended one man for one woman.” While I agree with monogamy, the Bible has many examples of men with more than one wife, and appears not to condemn this. Could you please explain how Genesis clearly teaches monogamy … ’

Answer

The clearest evidence that monogamy is God’s ideal is from Christ’s teaching on marriage in  Matt. 19:3–6. In this passage, He cited the Genesis creation account, in particular  Gen. 1:27 and  2:24, saying ‘the two will become one flesh’, not more than two.

Another important biblical teaching is the parallel of husband and wife with Christ and the Church in  Eph. 5:22–33, which makes sense only with monogamy—Jesus will not have multiple brides.

The 10th Commandment ‘… You shall not covet your neighbor’s wife [singular] …’ (Exodus 20:17) also presupposes the ideal that there is only one wife. Polygamy is expressly forbidden for church elders (1 Tim. 3:2). And this is not just for elders, because Paul also wrote: ‘each man should have his own wife, and each woman her own husband.’ Paul goes on to explain marital duties in terms that make sense only with one husband to one wife.

The example of godly people is also important. Isaac and Rebekah were monogamous—they are often used as a model in Jewish weddings today. Other examples were Joseph and Asenath, and Moses and Zipporah. And the only survivors of the Flood were four monogamous couples.

Polygamy’s origins and consequences

A very important point to remember is that not everything recorded in the Bible is approved in the Bible. Consider where polygamy originated—first in the line of the murderer Cain, not the line of Seth. The first recorded polygamist was the murderer Lamech (Gen. 4:23–24). Then Esau, who despised his birthright, also caused much grief to his parents by marrying two pagan wives (Gen. 26:34).

God also forbade the kings of Israel to be polygamous (Deut. 17:17). Look at the trouble when they disobeyed, including deadly sibling rivalry between David’s sons from his different wives (2 Samuel 13,  1 Kings 2); and Solomon’s hundreds of wives helped lead Solomon to idolatry (1 Kings 11:1–3). Also, Hannah, Samuel’s mother, was humiliated by her husband Elkanah’s other wife Peninnah (1 Sam. 1:1–7).

What about godly men who were polygamous?

Abraham and Sarah would have been monogamous apart from a low point in their faith when Hagar became a second wife—note how much strife this caused later. Jacob only wanted Rachel, but was tricked into marrying her older sister Leah, and later he took their slave girls at the sisters’ urging, due to the rivalry between the sisters. Jacob was hardly at a spiritual high point at those times, and neither was David when he added Abigail and Ahinoam (1 Sam. 25:42–43).

Why did God seem to allow it, then?

It is more like the case of divorce, which God tolerated for a while under certain conditions because of the hardness of their hearts, but was not the way it was intended from the beginning (Matt. 19:8). But whenever the Mosaic law had provisions for polygamy, it was always the conditional: ‘If he takes another wife to himself …’ (Ex.21:10), never an encouragement. God put a number of obligations of the husband towards the additional wives which would discourage polygamy. In view of the problems it causes, it is no wonder that polygamy was unknown among the Jews after the Babylonian exile, and monogamy was the rule even among the Greeks and Romans by New Testament times.