Why do we call the 1900s the 20th century?

It is because there have been 1900 years gone and we are in the next 100 years. 1900, marked the 1900th year and so the end of the 19th century. The 20th century started in 1901 and ended in 2000, not from 1900 to 1999. The year 2000 indicated 20 hundred years, so 20 centuries. So any time during the period from 1901 to 2000 was the 20th group of 100 years and so the 20th century. The 1st century ran from 1 to 100, the 2nd from 101 to 200 and so on, so the 20th was from 1901 to 2000.