Genesis 2:24
For this reason a man will leave his father and mother and be united to his wife, and they will become one flesh.
You are on the right track. Each relationship is unique (husband+wife). There can be multiple relationships (husband+wife1,husband+wife2,etc). This does not violate the Genesis verse. Those that use this verse in defense of monogamy are faced with two glaring problems
1) If this verse was a command for monogamy, then why did God not condemn plural marriage in subsequent ages? He had plenty of opportunity. Rather, God not only allowed for plural marriage, but gave laws concerning it, commands to participate in it, and God actually BLESSING individuals with plural families.
2) This verse was written by Moses, who had at least two, and possibly three wives.
************************************************************
1 Corinthians 7: 2
But since there is so much immorality, each man should have his own wife, and each woman her own husband.
This one is used a lot. I would encourage you to review our Resources page at this link, which speaks directly to this verse, and which i also reprint here:
http://biblicalfamilies.org/commonmisc#ref3
"The Bible says that every woman should have her OWN husband and every husband his OWN wife!"
"Now concerning the things whereof ye wrote unto me: It is good for a man not to touch a woman. Nevertheless, to avoid fornication, let every man have his own (Greek 'heautou') wife (Greek 'gune'), and let every woman have her own (Greek 'idios') husband. Let the husband render unto the wife due benevolence: and likewise also the wife unto the husband. The wife hath not power of her own body, but the husband: and likewise also the husband hath not power of his own body, but the wife. Defraud ye not one the other, except it be with consent for a time, that ye may give yourselves to fasting and prayer; and come together again, that Satan tempt you not for your incontinency. But I speak this by permission, and not of commandment. For I would that all men were even as I myself. But every man hath his proper gift of God, one after this manner, and another after that. I say therefore to the unmarried and widows, It is good for them if they abide even as I. But if they cannot contain, let them marry: for it is better to marry than to burn." 1 Corinthians 7:1-9
1438 heautou {heh-ow-too'} (including all other cases) from a reflexive pronoun otherwise obsolete and the genitive case (dative case or accusative case) of 846;; pron. AV - himself 110, themselves 57, yourselves 36, ourselves 20, his 19, their 15, itself 9, misc. 73; 339 1) himself, herself, itself, themselves 2398 idios {id'-ee-os} of uncertain affinity;; adj AV - his own 48, their own 13, privately 8, apart 7, your own 6, his 5, own 5, not tr 1, misc. 20; 113 1) pertaining to one's self, one's own, belonging to one's self
"Heautou - can be used in the place of the possessive pronoun autou in order to make the expression of possession more forceful.
Idios - In the New Testament the adjective (i.e. Idios - jl) - used as a possessive pronoun - has a more or less emphatic stress: (cf.) Matt. 9:1. In Matt. 22:5 the adjective is [used as a] possessive pronoun as it is in Matt. 25:14; the synoptic parallels to Matt. 25:14 (Mark 13:34 and Luke 19:13) have respectively autou and heautou instead.
In Paul's letters the often special stress of the adjective (as opposed to allotrios) sometimes has theological weight: (Here Rom. 8:32, 10:3 and 14:4 are listed as examples.) Through conjunction with hekastos (and that is the case in I Cor. 7:2 - jl) the individual relationship is underlined. (Here I Cor. 3:8 is given as an example.) For the relationship of the wife to her husband or, as the case may be, of the husband to his wife Idios is used in: Acts 24:24, I Cor. 7:2 & 4, 14:35, Eph. 5:22, Col. 3:18, Tit. 2:5 and I Pet. 3:1 & 5."
What does it mean to 'own' something?
What is the difference, if any, between the Greek words 'heautou' and 'idios'?
In Matthew 19:8, the Greek 'gune' is translated as wives and in 1 Corinthians 7:2 it is translated as wife, does that mean gune can mean either wife or wives?
What is the meaning of this passage? Is polygamy the topic?
A man and a woman own a house. They have, or possess, a home. Two people can own the same thing. Two wives can own the same husband. In a polygamous marriage each person has there own spouse. For example:
Matthew, Laura, and Betty are in a polygamous marriage. Each person has their own spouse(s). Matthew has Laura. Matthew has Betty. Laura has Matthew. Betty has Matthew.
There could very well be a reason why Paul used two separate words for "own". Heautou stresses the exclusivity of the possession, and idios the exclusivity of the relationship. In other words, the husband may say, "That is my wife, she belongs to me and me alone." The wife would say, "That is my husband, and I belong to him and him alone." The word structure, then, would very well leave extra room for polygamy. The passage is not about the number of wives a man can have, but about having of a spouse in the first place. Paul is showing us that we can avoid fornication by marrying, "for it is better to marry than to burn" with marital desires.