What is the rationale behind the minimum values for indicators?

Generally, the minimum values are set to the values that a society needs to survive over time. For life expectancy – 20 years is based on historical evidence (Maddison, 2010, and Riley, 2005), which indicates 20 years as the minimum. If a society or a subgroup of society has a life expectancy below the typical age of reproduction, that society would die out. Lower values have occurred during some crises, such as the Rwandan genocide, but these were exceptional cases that were not sustainable. See:
Maddison, A. 2010. Historical Statistics of World Economy: 1-2008 AD. Paris: Organization for Economic Cooperation and Development.
Riley, J.C. 2005. Poverty and Life Expectancy. Cambridge, UK: Cambridge University Press.
Noorkbakhsh (1998). The Human Development Index: Some Technical Issues and Alternative Indices. Journal of International Development 10, 589-605.
For both education indicators, the minimum is set to 0 since societies can subsist without formal education. For income, it is set at $100 per capita GNI, which is lower than the lowest value attained by any country in recent history (Zimbabwe in 2008). Should any country’s per capita GNI fall close to or below $100, the minimum will be changed accordingly.