Abortion is more visceral than the decline of marriage. Everyone who has held a baby understands the stakes of the abortion debate in a way that is much more motivating than the intellectual case against gay “marriage”.
SSM has strengthened my belief in marriage, as well as that of all those many, many same-sex couples who are now married. Has it weakened your belief? If so, how?
Do you mean “arguments” against gay marriage?
It has not, but I am far from the marginal case.
Your cite shows that marriage rates have been declining for 40 years (their chart starts in 1979); that decline predates the legality of SSM in any U.S. state by 24 years (Massachusetts, 2003), and predates the Supreme Court’s Obergfell decision (2015) by 36 years. So, it’s pretty spurious to say that societal acceptance of SSM is to blame for that decline.
If it strengthened the belief in marriage of liberals like me, and didn’t reduce the belief for conservatives like you, then whose belief did it reduce, and how?
In a democracy, a clear majority say same-sex marriage marriage should be legal.
Of course, you’re probably talking about a conservative “democracy”, where conservatives get to decide who can vote along with who can get married.
Furthermore, since the legalization of Gay Marriage, there has not been a single World War. Contrast that to not just one, but two world wars in the century previous. Clearly SSM is a great peace-keeping policy.
If it strengthens the belief in marriage, than why are marriage rates declining?
The decline is not monocausal. A country with a strong institution of marriage would not have entertained the idea of gay “marriage” in the first place. No one has claimed that it is the only reason or even principle reason marriage has declined. It is another step in the descent.
In a democracy votes count and not polls. There were 30 referendums that we won, most of them with over two thirds of the vote. There was nothing democratic about what our rulers did.
AFAICT from the Brookings link, the rate of decline has lessened in the last few years. The fastest rate of decline was long before SSM was part of the national conversation. So my supposition that legalized SSM will strengthen marriage has some support from the data so far.
BTW, the number of marriages actually went up in the U.S. in 2014-17, compared to the decade or so before. In the decade prior to Obergfell, the U.S. was consistently having about 2.1 million marriages per year; starting in 2014, it went up, and in 2016, there were 2.25 million weddings (a number that hadn’t been seen since 2005).
Of course, it’s also likely that a good-sized proportion of those additional marriages were same-sex marriages, or as @puddleglum would call them, “marriages.”
Red states have a strong showing when it comes to consuming gay porn. Blue states do too but the point is that you’d think few people would be watching gay porn in the Bible Belt but the opposite is true.
NOTE: That link is to Pornhub but it is an article and safe to view (unless you find the topic a problem).
Check your New Oxford Dictionary*. It is neither homophobic or transphobic, quite the opposite.
Or hover over the acronym and highlight it , then ‘look it up’. That’s what I did.

If our rulers on the supreme court would let democracy happen, it would already be illegal in many states.
According to the Gallop Poll, 48% pro-choice vs. 48% pro-life (5% undecided). Sounds to me like the Supreme Court is allowing democracy to take it’s course.
Marriages went up because of the population of people of marriageable age going up. The marriage rate per capita was in 2018, the last year of data available, the lowest in recorded American history.
Gay marriages are estimated to be about .33% of total marriages, so the proportion is not good sized.

Everyone who has held a baby understands the stakes of the abortion debate in a way that is much more motivating than the intellectual case against gay “marriage”.
Possibly true, but understanding the stakes does not lead all people to the same conclusion. 59% of abortions are obtained by people who already have children

The institution of marriage seems to be in decline just as we who opposed gay “marriage” predicted it would be. The data I have seen show that society is [bifurcating ]into those who believe in marriage and those who do not.
From the cite you gave:
Over the last few decades, family formation patterns have [altered significantly in the U.S., with long-run rises in non-marital births, cohabitation, and single parenthood – although in recent years many of these trends have leveled out.
The graph shown further down in that article shows a drop primarily between 1979 and 2000. Gay marriage was illegal in all states in the USA until 2004, and the Supreme Court decision legalizing it fully in the USA was in 2015. Whatever caused that drop in the late 20th century, it wasn’t gay marriage.
(Considering that there was no drop in marriages among the richest quintile in those statistics, it seems likely either that the drop was caused by relative lack of money, or else that not being married is likely to result in having less money.)
(Realized after typing this that kenobi_65 already said much of it, and iiandyiiii has also posted some of it.)
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So, puddleglum, can you explain why you put the word marriage in quotation marks?

Gay marriages are estimated to be about .33% of total marriages, so the proportion is not good sized.
So, if SSM is only .33% of total marriages, how can it be affecting the other 99.67%? That SSM is some waaayyy powerful stuff!
Help me out on another point. How does SSM get in the way of DSM*? How does it prevent different sex marriages*? If 2 men marry, how does prevent a man and a woman marrying somewhere else?