Since 10% is a pervasive myth, here’s one answer from Snopes: https://www.snopes.com/science/stats/10percent.asp
“The origins of the myth are not at all clear. Beyerstein, of the Brain Behaviour Laboratory at Simon Fraser University in British Columbia, has traced it back to at least the early part of the [20th] century. A 1998 column in New Scientist magazine also suggested various roots, including Albert Einstein and Dale Carnegie (“Brain Drain”). It likely has a number of sources, principally misunderstood or misinterpreted legitimate scientific findings as well as self-help gurus.”
My preference for an explanation comes from inadequate science in late 19th and early 20th century assessments of brain function, especially the cerebral cortex. They could tell that simple tasks only involved small portions of the brain at any given moment. And they were unaware of adult neuroplasticity which allowed people to resume functioning after mild brain injury. They were also unaware of major function of glial cells. These misunderstandings shortchanged the complexity of brain function and were popularized as myths.
The myth is probably reinforced by research on degenerative disorders. For example, symptoms of Parkinson's disease develop only when there is 80% or more loss of dopamine neurons in the nigrostriatal pathway. This could be misinterpreted as demonstrating that 80% or more of the neurons in that pathway are not normally used. Obviously a lot of redundancy is built into the brain to prevent minor insults causing loss of function. The suggestion that people can use more of their brain is based on a misunderstanding of these facts.