Why are population projections so inaccurate? UN in 2015: India's population will surpass that of China in 2022.

Source: https://www.telegraph.co.uk/news/worldnews/asia/india/11770757/Mapped-India-predicted-to-become-worlds-most-populous-country-by-2022.html

UN in 2017: India's population will surpass that of China in 2024.

Source: https://timesofindia.indiatimes.com/india/indias-population-to-surpass-that-of-chinas-around-2024-un/articleshow/59257045.cms

UN in 2019: India's population will surpass that of China in 2027.

Source: https://www.indiatoday.in/india/story/india-population-china-united-nations-report-world-1550962-2019-06-18

No one expects population projections to be 100% accurate but I didn't expect them to be this inaccurate either. What are the possible reasons for the UN getting this wrong so many times and by a margin of several years?
This is because most of these projections are based on extrapolation (in fact almost all forecasting is based on extrapolation) which is inherently extremely inaccurate. 

Consider this simple example:

Let’s say that we know that person who gets breast feeding for 3 months will have height 150cm person with 4months 160cm and 5months 170cm. Now based on this it is very easy to estimate that the relationship in this small sample would be:

$$H=120+10M$$

Where $M$ is months of breastfeeding and $H$ height in centimeters. Now based on this relationship we could let’s say expect that someone with 3,5 months of Brest feeding will have 155cm and that would be quite accurate. But see what happens if we start to extrapolate that is to plug there numbers further and further out of our sample.

Let’s start with 6 months that would give us height 180 - reasonable. Let’s try 8 months it would give us 200 still reasonable but let’s try 20 months it would give us height 320 which for human might not even be possible.

The takeaway is that the relationships can change. Between 0-8 months the relationship can be nice and linear but at some point the relationship flattens so extrapolation too far outside the sample will lead to wrong prediction.

The same hold for population growth. If you predict population growth 12 months in advance then that can be easy as the relationship should not change that quickly. However, 10 years ahead it is very likely that the relationship that was estimated based on past birth rates simply changes. This could be due to the fact that the previous estimations were done from past observations at smaller total population (since birth rates can be different at different population levels). Or also because preferences of people changed in unpredictable manner. Or also because many of these projections can use some auxiliary forecasts of for example GDP growth that have their own margins of error.

Hence, it’s not really that surprising the projections were wrong. In fact I could even say given how difficult forecasting and extrapolation is its surprising they are not even more off then they actually are. 

Also to really make sure the forecasts were wrong you also have to go to those reports and check their margin of error if one of the sources forecasts that birth rate will be 4% with margin of error of 3% then you can’t say real birth rate 7% was off as it’s covered in margin of error. Statistics is in end only exercise in probability no estimate is certain it’s always just a distribution.