> A 100x100 thumbnail that was reduced from a 1000x1000 image might have pixels which are derived from 100 samples of the original image (e.g. a simple average of a 10x10 pixel block). Or other possibilities.

And if a downsampling algorithm tries to approximate a point sample, it'll give you a massively increased chance of ugly moire patterns.

The audio equivalent is that you drop 3/4 of your samples and it reflects the higher frequencies down into the lower ones and hurts the quality. You need to do a low-pass filter first. And "point samples from a source where no frequencies exist above X, also you need to change X before doing certain operations" is very different and significantly more complicated than "point samples". Point samples are one leaky abstraction among many leaky abstractions, not the truth. Especially when an image has a hard edge with frequencies approaching infinity.