If you consider the effects of the winners always writing history, you can look at the way we overlook the actions of certain despots and highlight those of others depending on who were the winners and losers. How many school children can immediately shout out the evils of Hitler but don't know about Stalin's pogroms or the mass murders committed by Pol Pot with weapons supplied in part by the good old US of A? It is dangerous because those in power always get to skew things their way to deflect blame, to influence society in rather powerful ways.
One of the most difficult things to teach students is the idea that history is not based on facts, but is based almost entirely on interpretations of the facts and the actions of people in the past. If we only allow the winners to make those interpretations, it becomes easy to accept one viewpoint and not raise objections. There are people out there who say that our participation in WWII was absolutely a mistake. Of course the accepted view is that it was a moral necessity, but without the other side, who would raise objections about our firebombing Tokyo or interning Japanese citizens without any good reason to do so? Without the other side getting to have their input we move towards a 1984-like state where everything is edited to fit with the vision of those in power.
This is certainly not a new concept as Phillips points this out quite a long time ago but we are still struggling with it today.