A wild guess? I think it's from a trustworthy source: it seems to be taken from Edward Wilson, "The diversity of Life". Of course there is a high uncertainty in this number. But where is your threshhold what rate is no longer acceptable? A hundred species a year? A thousand? Ten thousand? A hundred thousand? One?
Wriggle out option 1: We humans have the right to "make use" of this planet! Click
Wriggle out option 2: Why care - it does us no harm and nature will regenerate! Click