Is this study reliable?
We often get questions on Skeptics.SE about one particular study, asking if it "proves" some controversial claim.
The short answer, without even looking at the study, is "No. One single study is not reliable. Studies are often wrong. Unfortunately, sometimes it is all the evidence we have."
If we have the luxury of more than one study of a phenomena, and they disagree, we can use a systematic review (or even better, a meta-analysis) to try to resolve the dilemma. More on that in a moment.
This particular study has received some criticism.
For example, Philip N. Cohen, [now] Professor of Sociology, wrote a blog article in 2013 criticising several aspects.
He claims the sample size is actually about 85 gay-father kids and 194 lesbian-mother kids. That should be enough to get statistically significant results for large effect sizes, but it is considerably smaller than the headline figure of "20% of the Canadian Census" might suggest.
He claims the sampling has selection bias by including 17-22 year olds that still live with their parents, while excluding those who moved out.
[Note: This means even if the results are "statistically significant", they are still biased.]
He claims the odds ratio presented is misleading:
Anyway, the paper does provide the marginal effects, which show that the children living with gay parents have graduated from high school at an adjusted predicted percentage 6 points lower than those living with married different-sex parents
Meanwhile, Mark Regnerus, [now] Professor of Sociology, wrote a 2020 article, Understanding how the social scientific study of same-sex parenting works defending his own 2012 paper that found differences in children of same-sex relationships. That paper caused some controversy in the social science community, with open letters attacking the research and defending it being signed by dozens or hundreds of scholars.
Regnerus argues that population studies are hard, and subject to coding errors, that the differences in outcomes are hidden in the choice of factors to control for and sampling strategies, and accuses fellow scientists of not being neutral in their choice of papers to criticise:
As a result, it is difficult to conduct solid social science research on such topics, when the world of scholarship on sexuality has tacitly ruled some conclusions more worthy of publication than others. Scientific neutrality is out. Political expedience is in.
So, we can see that individual papers on this subject have triggered a lot of criticism and defence, reinforcing that we should treat each paper with care.
But back to systematic reviews...
In 2022, a team published Family outcome disparities between sexual minority and heterosexual families: a systematic review and meta-analysis.
They looked at 34 studies (16 for the meta-analysis) for a large number of outcomes.
Most of the family outcomes are similar between sexual minority and heterosexual families, and sexual minority families have even better outcomes in some domains. Relevant social risk factors of poor family outcomes included stigma and discrimination, poor social support and marital status, etc.
However, the question here is about academic achievement, so let's look at what they found there.
We conducted a narrative synthesis of six studies on children’s educational outcomes. Four studies indicated that children from same-sex couples appear to have the higher rate of grade retention, lower graduation rate or worse educational attainment than children from different-sex couples. On the contrary, two studies reported that children in sexual minority parent families outperform children in heterosexual parent families on standardised test scores, high school graduation rates, college enrolment, and school/academic competence.
[Note that the original study in the question is one of the four.]
They did not conduct a meta-analysis on this data, so it isn't clear how strong each study is, but as you can see: The result is unclear:
Four studies found children of same-sex parents do worse at school.
Two studies found they do better.