In your first paragraph, you're saying that the critique claims, in essence, "We don't know there's a correlation between death by suicide and being gay," and y

In your first paragraph, you're saying that the critique claims, in essence, "We don't know there's a correlation between death by suicide and being gay," and you're saying that claim is false, because there is evidence that suicide rates among gay people are higher than the general population. But that's not what the critique is claiming. What it's claiming is that this JAMA study, in particular, fails to establish the association it claims to establish. And in your second paragraph, you're saying that the critique is not saying, "Hey, this study is flawed," but is saying, "I hate gay people and I don't want them to think that their sham marriage is in anyway equivalent to my real marriage." Briggs makes no secret of the fact that he rejects same-sex marriage, but the vast majority of his post is devoted to flaws in the study, not to his own personal objections to same-sex marraige, and although his ideological views probably are a motivating factor for his scrutiny of the study, that doesn't necessarily invalidate the points he makes.