The problem is essentially this: since pagerank is basically the probability that a random walk through the link graph will end up on your site, linking back to yourself, and no other websites, gives a big boost to your pagerank because a random walk will get stuck on your site. Of course it’s easy to just ignore self-links, but you can get essentially the same effect through clique-like groups of websites and this can be more difficult to detect.
What’s interesting is that an algorithm based on how electrical current flows (so a link is a one-way resistor, i.e. a resistor in series with a diode) would not have this problem. Attaching a conductive loop to some point in a circuit does not change how current flows. Electrons don’t get stuck in loops because they don’t drift around randomly, they move from lower voltage to higher voltage.