Historical evidence supports that a decrease in mortality rates is followed by a decrease in birth rate. Here, check out the data for yourself[1]
The theory of population growth leading to resource depletion is fairly old. Thomas Malthus published this in 1798[2], but guess what: we're all still alive, despite growing over 7 billion in size, and the empirical evidence debunked this theory. There are a fairly large number of theories why this didn't happen, but that's off topic.
My point is:
- The shortage of resource because of over-population is an old theory, but we've seen no evidence to it yet.
- Population growth eventually slows down when the mortality rate decreases.
- The population growth rate is expected to begin slowing[3]
- Colorful animations help people understand a point, but that doesn't necessarily mean they're wrong.
[1]: https://ourworldindata.org/grapher/Demographic-Transition-Mi...
[2]:https://www.intelligenteconomist.com/malthusian-theory/
[3]:https://esa.un.org/unpd/wpp/Graphs/Probabilistic/POP/TOT/