This is a falsehood based on a half-truth, all of which is designed to support the lazy dad myth. Dads put in more paid work hours and moms put in more hours at home. This speaks to the Mad Men-era sexist structures that make it tougher for women at work and tougher for men to get equal time with their families at home. (This is the focus of my book. Read the Introduction and Chapter 1 here.)
The “full time” assertion creates confusion. In records and studies, working “full time” means at least 30 hours a week. So if a mom works 38 hours professionally and a dad works 46 hours professionally, then sure, the mom ends up doing more housework and childcare. But the dad is working just as hard to keep bills paid.
This is also why the wage gap — which is real — hurts everyone, including dads. When moms aren’t paid what they’re worth, dads work even harder as breadwinners, and the sexist cycle continues.