The worry is still easy to understand I think. Suppose you are a programmer or a project manager and you have come to think that your skills are valuable, i.e., they are rare and someone will pay for those skills so you find opportunities to participate in the economy. Suppose further you believe that some AI programs will be able to produce the programs you could produce, it makes sense to be worried as you would immediately think will you be laid off and have trouble finding ways to participate. This is the same phenomena every disruptive breakthrough puts communities of people through every so often.
That said, as I said I find the discussions on AI generally incoherent. I do not believe programmers or teachers will be obsolete in the foreseeable future (probably ever) nor is it a bad idea to put certain jobs into the hands of machines; a lot of the jobs are terribly boring and should be replaced. I would guess that whatever the disruption, we are likely open new rooms to develop new skills that we'll see over time.
As a side point yes I agree in some areas, like art, people will always find more value in originality and creativity coming from a human. I'm convinced we will always find what Monet did more beautiful than what some robot can do. But that doesn't apply to other fields like programming, or product management, or cleaning.