Not just any time it's copied or generally over time, but each playback can degrade the quality. Record pins erode the channels, magnetic heads affect the strength of the magnetic field they read.

Reads, copies, and time don't (necessarily) degrade digital media, even with lossy compression (time can, but any time it's copied, it resets the clock to as good as the media can give; analog doesn't get that reset). Lossy compression only degrades it on conversion and there's a bunch of control over the shape of that degradation (with the intent of it not being detectable to our ears, though it obviously also depends on the bandwidth available).

That is an actual fair criticism. Well, part of it. All of our current digital media technology actually degrades over time faster than analog ones, but they're so easy to copy that it's not really a problem for things that people like to make copies of. It is a problem for archiving though. I wasn't trying to argue that digital has no advantages. Just that it's not magically better in every way.