Maybe I should ask why the LPI report uses such a weird number instead?
Take your population of 10,000 rhinos. It drops by 90% to 1,000. The next year it increases by 90% to 1,900. If you did a normal average of the changes, you'd get (-90%+90%)/2 = 0% change. That's a useless number because there has obviously been some major changes between the two years.
If you use a geometric average you'd get sqrt(0.1 × 1.9) ~= 0.436 or roughly a 56% average decrease. This is more meaningful than saying the average change was 0%.
However, you can't use that number to work out how many rhinos there are. It's used to measure an overall trend. If the average decrease gets smaller, it would mean more populations are increasing and less populations are decreasing. Overall, that's good. That's what the number is meant to be used for.
If the average decline next year is 68% then that'd mean we're doing something right because last year the average decline was 73%. What are we doing right? Which populations are better? Which are worse? You can't tell from the average. It's just a general marker of the overall trend.