JOEL - It will be very difficult to help anyone else feel the same as you do if they have not first received a testimony of the divinity of the restored Gospel and the importance of latter-day prophets. Without this most people outside the Church (and many within the Church) will always be bothered by the doctrine because it goes against what they have been taught or how they personally feel about it.
So the first thing you should tell them is that unless they believe in latter-day revelation from God, it will be difficult for them to understand the reason for it.
There are a few other things you could say to them. For one thing, evidence suggests that God condoned polygamy at certain periods in history. The Bible records that Abraham, Isaac, and Jacob all had multiple wives, with God's approval.
But, according to the Book of Mormon, God Himself disapproves of polygamy, except in special circumstances, because it is so painful to his daughters.
"For there shall not any man among you have save it be one wife and concubines he shall have none. For I, the Lord God, delight in the chastity of women. And whoredoms are an abomination before me" (Jacob 2:27-28).
"For behold, I, the Lord, have seen the sorrow and heard the mourning of the daughters of my people...because of the wickedness and abominations of their husbands.... Ye have broken the hearts of your tender wives and lost the confidence of your children...and the sobbings of their hearts ascend up to God against you" (Jacob 2:31-32).
But there are certain times when He commands it to be practiced.
"For if I will, saith the Lord of Hosts, raise up seed unto me, I will command my people; otherwise they shall hearken unto these things." (Jacob 2:30)
The law of plural marriage was revealed to Joseph Smith around 1831 and the revelation was given to him under strict commandment from God to live it. At the time the doctrine was announced to the membership of the church Orson Pratt explained, "the constitution gives the privilege to all the inhabitants of this country, of the free exercise of their religious notions, and the freedom of their faith, and the practice of it." In their opinion this included the practice of plural marriage. At the time there were no laws against it. He also said that, "marriage was ordained of God as the channel for spirits to acquire mortal bodies and that through plural marriage worthy priesthood holders could raise up a numerous righteous posterity unto the Lord." (Millennial Star, 1853). So, the primary reason was to help as many spirits as possible to obtain their bodies, be raised in good families, and to build up the kingdom of God on earth. The best way to do that and get it started quickly with only the few worthy saints that were available at the time was to live the law of plural marriage. When the need no longer existed to "raise up seed unto me", and when the laws of the land changed, making it no longer legal, the Lord removed the requirement for the saints to practice it.
"Wherefore I, the Lord, command and revoke, as it seemeth me good; and all this to be answered upon the heads of the rebellious, saith the Lord." (D&C 56:4)