I wouldn't say this is necessarily true, it's more that they have other things to care about. We can't criticise developing nations for enjoying the same luxuries we did a hundred years ago. It should be our (first world) job to ensure they get the same benefits from fossil fuels as we did, such as transport freedom and easy access to electricity, but using environmentally friendly technology. Unfortunately, we can't even get ourselves away from fossil fuels quick enough, so this is likely not going to happen.
Also, developing countries emit far fewer emissions per capita when you look at consumption-based emissions [0]. This isn't necessarily a problem with the number of people, it's a problem with the type of lifestyle people want and expect. Even if population increase stopped entirely climate change would get far worse if everyone on Earth had a 1st world lifestyle of red meat, SUVs and yearly holidays.
Population increase is obviously a problem but it's an overstated one. If everyone went vegetarian, which is going to have to happen at some point, the planet can sustain 10 billion people [1], which we're only forecasted to hit in 2100, if we even a) make it that far and b) don't see a reversal in population growth, which has been predicted.
[0] https://ourworldindata.org/global-inequalities-co2-consumpti... [1] https://www.livescience.com/16493-people-planet-earth-suppor...