The problem really comes down to the fundamental issue fo what marriage is.
When you allow for same-sex "marriage" you are left with only two options:
(1) Have (at least) two different kinds of marriage, one for opposite-sex couples and one for same-sex couples. This is part of the reason why some people were pushing the marriage-look-alike alternative "civil unions." The problem is that our current ethos of equality will never allow this, as it is "separate" and therefore not "equal."
(2) Redefine marriage for everyone by turning it into a gender-neutral institution. The whole concept of marriage as it exists in our culture is based on the complementarity of the sexes. Such terms as "bride" "groom" "husband" and "wife" are explicitly based on heterosexual unions and do not really fit into same-sex unions. The only way to truly make the unions equal is to basically redefine the terms we use and the way that we think of heterosexual marriage in order to conform it to the same-gender model. Of course, this is what a lot of people want; traditional marriage is "sexist" or "heterosexist" to them, and terms such as "bride" and "groom" are "heteronormative," which is apparently supposed to be a bad thing.
That is ultimately what this story is about; the inexorable result of same-sex marriage is to define normal marriage down so as to make it equivalent to the ame-gender variety, and to take all of the particulars that make marriage what it is and to eliminate them. And they scoff at the idea that same-sex marriage will weaken marriage: "how," they ask, "will letting more people get married weaken marriage?" The answer, of course, is that it will weaken marriage by removing the particulars that make marriage marriage.
If I were to insist that Rush Limbaugh's (or Randall Terry's) ideas were to be labelled "feminist" or that Jesse Helms be placed in the camp of the "anti-racists," the leftists would have a field day. Obviously in that case they can see why increasing their nominal number weakens, and not strengthens, them. But in the end they do not care about marriage, or see it as a mere legal contract no different than, say a business partnership, so the idea that the same principle applies is completely foreign to them.
That is all.