How Do You Explain That Machines Won't Really Think Like People?

You could try a subtle approach, as one Oxford researcher did. He proposes a different model from "artificial general intelligence" (think like people). Rather, he introduces "Comprehensive AI Services" (CAIS), relying on the work of Eric Drexler, author of Engines of Creation: Instead of relying on some unforeseen breakthrough, the CAIS model of AI just assumes that specialized, narrow AI will continue to improve at performing each of its tasks, and the range of tasks that machine learning algorithms will be able to perform will become wider. Ultimately, once a sufficient number of tasks have been automated, the services that an AI will provide will be so comprehensive that they will resemble a general intelligence. One could then imagine a "general" intelligence as simply an algorithm that is extremely good at matching the task you ask it to perform to the specialized service algorithm that can perform that task.