Agreed on the methods used for studies. However, there are many studies that are conducted using past subjective data and given a large enough sample size, reasonable conclusions can be reached.
I read the study linked below and, as predicted, when comparing apples to apples (mom and dad both have the same level of support, financial resources, etc.) the outcomes for the children are the same or similar. I was merely trying to point out that single mothers have been the default since time immemorial, so the sensationalized study saying outcomes for children of single fathers are better is simply that - sensationalized. The media doesn't pick up on a boring study saying that outcomes are the same given similar circumstances - that's not inflammatory. But they'll do decades or more of damage by spreading the inflammatory findings far and wide.
https://pubmed.ncbi.nlm.nih.gov/36554609/#:~:text=Results%20from%20analyses%20of%20the,;%20single%20fathers;%20single%20parent.
https://rcdvcpc.org/facts.html#:~:text=Abusive%20fathers%20are%20more%20than,perpetrated%20by%20a%20trusted%20adult.