Birth control being invented and having access to it are 2 different things. Even the ability to afford it is a barrier to use. Some countries simply have none available, or having a large family is necessary to help even parents retire. Not all countries have a social safety net.
As others have said, even if it was available, a couple having 3-4 kids increases the population. Living longer increases the population if more babies are being born than seniors dieing.
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