What is it about k-means that means it doesn't work on other distributions? I find it easy to come up with other (contrived) distributions where K-means produc

What is it about k-means that means it doesn't work on other distributions? I find it easy to come up with other (contrived) distributions where K-means produces the results that a human would produce. E.g. disjoint (and distant) circles, each containing uniform random distribution of points. Can you explain what you meant in more detail?