Why?
Suppose you were counting out one hundred pennies to make a dollar. The 100th penny you counted would be the last penny counted toward the dollar. Similarly, if you were counting out two thousand pennies to make twenty dollars, the 2,000th penny would be the last one counted, the end of the series.
Since we begin counting with number 1, centuries begin with years ending in 1, not with years ending in 0. It doesn't make sense to begin counting with zero, because zero stands for the absence of anything to be counted.
In the year 2000 we can celebrate the 100th year of the 20th century, but we'll have to wait until 2001 for the first year of the next century.