alt Hacker Newsyou were probably scraping the thick transparent side, not the side with the label? the data is immediately under the label. the clear side can be surprisingly scraped up and still read properly, though I'm not sure how!! I have some CDs that I thought were ruined because of how scratched up the underside is, and they play just fine. Pretty sweet! Then I have one or two where the label side got a scratch taken out of it, and indeed, you can see right through the disc at those points - unrecoverable damage. Conversely a scratched up underside can simply be buffed/polished smooth and the disc will read good as new. I actually have one disc that cracked in half (a singular crack from the center to the outside edge, not spanning the total diameter of the disc)... and it actually plays without any skips (though surely depending on quality of the player and its resilience to read errors). I couldn't believe it at the time. A single piece of masking tape to hold the edge together was a sufficient "repair".
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CD pickup detects changes in the reflected light due to the reflective pits. As long as the scratches are significantly bigger than pits they will create lower frequency attenuation to the reflected light which won't affect the high frequency signal coming off pits. You will get occasional errors when crossing into and out of a scratch but that's just a few samples, likely those won't even make it through through the speakers. I have not tried but I imagine a very fine sandpaper could create the scratches at high enough frequency to interfere with the pickup.
But the label side is indeed very fragile as you can easily damage the reflective pits, only covered by a layer of paint. It's as same as a simple mirror, where the thin layer of reflective metal is very well protected from the front but is only covered with paint in the back.
I worked in a CD foundry in the early 1990s. Scratches that were not tangential (perpendicular to the radius) were irrelevant, as the basic CD encoding scheme provide something like (IIRC) 30+ bytes of data parity protection. If the scratch width along the track wasn't longer than that, it didn't exist.
If it did exist, some toothpaste rubbed tangentially around the CD on your fingertips was often enough to buff it out, at least as far as the 30-byte limit cared.
It was a phenomenal jump in data integrity, built in at the recording level. Sure, you could encode even floppies with that scheme... but your computer didn't, natively.