Modesty is a much overrated virtue

The American economist John Kenneth Galbraith says in his memoirs that he had thought that the most likely inscription on his gravestone would be: modesty is a much overrated virtue.
An interesting observation. In many of our cultures it is taken for granted that modesty is a positive virtue, whereas the opposite is bad, be it what it may be. But is modesty really so important? Isn't pride, or self-confidence just as important? Especially in today's world? Shouldn't we place at least as much emphasis on teaching kids to be self confindent and proud of themselves as we do on being modest? Americans are good at this. Europeans, especially continental Europeans in the Germanic and Slavic regions are not so successful.
Of course the opposite of modesty should never be too bragging. But why the emphasis on modesty, and why not on pride?