Two young love-birds are getting frisky, guy says "don't worry, I'll marry you", they get down to business, and then he bails. Poor young girl is now damaged goods. She's plausibly even pregnant, but even if she's not, her marriage prospects are down. She can sue the guy for breach of marriage promise.
Then the law changes, breaching a marriage promise is no longer something you can sue for. In the same situation, the guy's promise to marry the girl no longer hold the same weight because she can't sue -- so they come up with a bond instead: An expensive gift that is forfeited if the guy doesn't keep up his promise to marry.
Besides, if you need that kind of collateral before you can trust a guy, maybe you should be looking for another guy in the first place. It also doesn't explain why people who don't have premarital sex still want diamond rings.
So all in all, not a great theory.
Also, I don't understand the supposed logic behind a change in marriage law and a rising demand for diamonds.