Because of sharp edges where edges should be sharp. JPEG compression doesn't allow it by its very nature.
The compression artefacts I think you are thinking of are likely the result of someone not setting the quality parameter appropriately. For text or charts, you're best off at 100%, but you can easily get away with lower values for most photographs. Granted, not an issue with PNG, but JPEG isn't so bad when used properly. (and typically does have huge file size benefits)