Why is there a discrepancy between the time it took for modern man to reach its first billion and the time it took for him to reach his 2nd billion?
Because it is an (approximately) exponential growth in population.
The time required to reach each successive billion would also fall I guess, though other factors have come into play since the advent of effective contraception (thankfully) and the rising notion that women are in charge of their own bodies & reproductive rights are not a God-given patriarchal right.
This is an interesting graph to ponder:
And this gives a broader perspective: