I first heard the claim that house dust is mostly made up of human skin on a TV show, when I was a kid (probably Cheers, where Cliff makes this comment at the beginning of a Season 9 episode), but even today I often hear this "fact" being repeated.
From Better Health:
The main component of dust is shed skin flakes
MicrobiologyBytes even gives a percentage:
About 80% of the material seen floating in a sunbeam is actually flakes of skin
But according to the Fortean Times:
There’s no evidence to suggest that dust is mostly made up of any one ingredient; rather, it is a delightful salmagundi or potpourri of everything that is likely to be drifting around your house.
The precise ingredients and proportions present will presumably depend in part on where you live, as well as how.
Is house dust mostly made up of our shed skin flakes?