Brynjolfsson and McAfee’s mistake comes from considering only first order effects of automation where the machine replaces the worker. But when a machine replaces a worker, there is a second order effect: the organization using the machine saves money and that money it flows back into to the economy either through lower prices, higher wages for the remaining workers, or higher profits. In all three cases that money gets spent which stimulates demand that other companies respond to by hiring more workers.
It's the traditional argument that demand simply shifts to new goods and services. But it relies on the traditional assumption that new needs are similar in economic terms to the old ones. In the example above, what of the higher wages for the remaining workers induce them to take more leisure, so total wages remain the same or even fall? That has not happened much to date, but it is a matter of taste rather than economic law.
The fundamental issue is how and when things fall outside the monetary economy, so the flow above springs a leak. I keep arguing that more and more of the things we value as we rise up the hierarchy of needs are harder to package in monetary terms, because they are not excludable nor rival goods. As the underlying nature of the economy changes, our institutions have to adapt too.