This above graphic comes from an analysis by Slate magazine of marriage rates in jurisdictions which have legalized marriage equality (Massachusetts, Iowa, Vermont, Connecticut, New Hampshire and District of Columbia) versus the national marriage rate. Do you see a trend or correlation? Me neither!
Neither does Slate, according to "Does Gay Marriage Destroy Marriage?":
The piece also goes on to look at divorce rates in the states where same-sex couples can get legally married (and divorced) right now to try to determine if such activity has any impact on the divorce rates of opposite-sex couples. The data just does not indicate that there is any impact of marriage equality on divorce or marriage rates in a state, unsurprisingly. What a shock, another talking point by religious extremists and heterosexual supremacists turns out to be obviously false.
Hat/tip to Americablog