Availability of education and basic needs is inversely proportional to birthrates.

This is a lie. It's a lie promulgated by wealthy interests to fight against economic redistribution. You can only reach the conclusion that wealth has no impact on birth rate by making inappropriate comparisons between countries. But when you look within countries, the true relationship is revealed.

There is no relationship between wealth and number of kids....until you reach an income level of $300k or so. Then, there is a very strong correlation. It makes sense. In the US, that's about the level of income you need to really be insulated from the worst aspects of the US's economic system. At that point, you can afford to send your kids to a decent school. You don't have to worry about going bankrupt from health care costs. You can likely afford to have a parent stay home if necessary. At that income level, you're able to simply purchase the level of stability that would come with a proper social safety net. And once people have some stability and security, they start having kids.

You're forgetting another portion of the calculation: amount of resources, and resource generation rate.

Take food for example. We have, and create, far more food than is needed. If that rate continues, we can theoretically keep pumping out people until the birth rates and food generation rates converge.

The actual problem, as it stands currently, is not the amount of resources, or how quickly we can create them: the problem is how they are distributed.