This "myth" (my humble opinion shared by many others here) comes from Christ's pronouncements on divorce, in Matthew 19. It requires looking at the passage with the express understanding that marriage = monogamy only. The reasoning is essentially circular. Examine it for yourself:
The Pharisees also came unto him, tempting him, and saying unto him, Is it lawful for a man to put away his wife for every cause? And he answered and said unto them, Have ye not read, that he which made [them] at the beginning made them male and female, And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh? Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder. They say unto him, Why did Moses then command to give a writing of divorcement, and to put her away? He saith unto them, Moses because of the hardness of your hearts suffered you to put away your wives: but from the beginning it was not so. And I say unto you, Whosoever shall put away his wife, except [it be] for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery."
The interpretation you have been presented with assumes a word not used. We would read the portion of Matthew 19 that they refer to this way:
For this cause shall a man leave father and mother, and shall cleave (only) to his wife: and (only) the twain shall be one flesh? Wherefore they are no more twain, but one flesh."
The two italicized "only" usages are not present, but are assumed to be there by the readers that tell you this is true. Their assertion also depends on the following:
Moses because of the hardness of your hearts suffered you to put away your wives: but from the beginning it was not so."
This is also twisted. The phrase "hardness of heart" is generally the same as just saying "sinful condition." To paraphrase what they think this means it would be:
Moses (on his own) because of the (hardness of the husband's heart) suffered you to put away your wives: but from the beginning it was not so. (Moses sorta changed things on his own here, but God really meant divorce never to happen and it is only because husbands are sinful that they divorce)."
Yet this is in direct conflict with an earlier passage in Matthew, the very first Chapter as a matter of fact, and the first meaningful comment in the Gospel of Matthew after the Genealogies he gives.
Then Joseph her husband, being a just [man], and not willing to make her a publick example, was minded to put her away (other versions use "divorce") privily."
It does not say "Joseph, being a sinful man, was minded to put her away" but "Joseph, being a JUST man." The Greek word translated to "Just" means "observing the DIVINE laws." So they are wrong on both counts. The word "only" is not used in the places I say they use it in assumed fashion, they just assume it based on their circular reasoning and cultural conditioning.
Next, they rip Moses as a false prophet, which invalidates the whole foundation on which the Gospel is built. Jesus keeps the law and states it is God's law, not part of it being Moses editorializing and part being God's law, but all God's law. He does this most definitively in Matthew 5. We know that the obedience to DIVINE law is what spurs Joseph to seek a divorce, not his own sinful hard heartedness. Notice we're staying in Matthew for this whole explanation.
Lastly I'll deal with their most credible grounds for stating this passage deals with polygyny and Jesus denying it as marriage:
Whosoever shall put away his wife, except [it be] for fornication, and shall marry another, committeth adultery."
This was a shocker to the Jews as they did not see men as "committing adultery" by doing anything to a wife of their own. Adultery by their definition occurred only in the body of a woman, in her sexual organs. Literally. The only other kind would be the imagining of or desire to commit that act, the sin of adultery of the heart. A concept they did understand through the law before Christ. Let's go to Jesus again, and Matthew's gospel, also in Chapter 5, where he talks about the law and, oh, adultery again:
But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery."
The last part echoes entirely Matthew 19 (or more rightly, Matthew 19 echoes Matthew 5). But what of this first part? The part where the man "CAUSETH his wife to commit adultery?" This seems different and contradictory. How does a woman commit adultery unless she actually does it in heart or mind or body?
In my humble opinion, it is because this passage does not contradict Matthew 19, or confuse it. If the adultery only occurs in the organs of the woman, and the sin of heart is the imagining or desiring of such an act, then Christ is saying the same things in Matthew 19 and 5, both of which help us understand the other. Yes, the adultery occurs in the woman's body, but Matthew 5 tells us the faithless husband who divorced his wife, caused it. If you cause it, are you not responsible for it? Thus in Matthew 19 the husband essentially "adulteries" his ex wife that he divorced unjustly. By God's law given to and through Moses, a divorced woman was her own free agent. It was clear she COULD marry again. Let's lay aside for the moment whether she ought to or not, she clearly could.
Whose sin was it then if the man caused her adultery? The man's, per Matthew 5, for he caused her. So Matthew 19 then says:
Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth an improper invasion of the ex wife's womb."
We would also know from Exodus 21 that he had done much the same thing as turning her into a concubine (a woman who was a wife though not of marriage) and then replacing her (which Exodus 21 says frees her entirely).
It's in the understanding of what Jesus meant by committing adultery against a woman that those who claim this interpretation of their most valid argument. After all, classically, as a Jew, you would think that to be entirely impossible. I think Jesus just said that if you made it happen, you take responsibility for it. If we define adultery as the defilement of a wife's womb, then the passage says that the husband defiled his own wife's womb. We would assume this would be because she has no property, there were no jobs other than harlotry and she would then seek to become the wife of another man for survival. Don't even think she left the house with her own sons, she didn't. She just went out. She could go back to her father's house, but sometimes that too was impossible. She would most likely just go to be another man's wife, and that was the best and most righteous possibility for her. Jesus, in my view, places the responsibility of the sin which then occurs in her body, on her faithless former husband. The woman's womb then merely becomes the geographic area where the sin takes place, and she is not the sinner.