It's because we tend to think in terms of gestalts, and those don't play well with reductionist approaches. It's only a contradiction if you assume that we apprehend all the constituent pieces of the world at once, rather than the abstract whole.
Treating a pile of sand as an accumulation of individual grains which can be precisely abstracted through induction is an unnatural mode of thinking. Without focusing our attention on it, it will remain a single, fuzzy abstraction. That we see no clear distinction between these two modes seems more a neurological phenomenon than a philosophical one.