Firstly, I don’t know where you are getting your data from, but Brazil’s birth rate is NOT considered high by any standards. Data from the World Bank shows that Brazil’s birth rate (2015) is 14.2 births per 1,000 inhabitants. That is very close to European countries such as France (12.0), the United Kingdom (11.9), Sweden (11.7), and other developed economies such as the United States (12.5) and Australia (12.1). For comparison, most African states would have what is considered a ‘high’ birth rate — South Africa, which is a developing economy and richer than many other countries in that continent, reaches 20.2 births per 1,000 inhabitants. Several other African countries, such as Angola, Mali, Niger, Uganda, have their birth rates at over 40 per 1,000. So I don’t know what you consider ‘high’, but Brazil is probably far from there.
But it was not always as low as it is today. In fact, less than 20 years ago (2000), Brazil’s birth rate was around the 20 per 1,000 inhabitants. While this is still not particularly high, if you check the stats of just a few decades prior to that, it was closer to 30. The main reasons for the previous high numbers are that Brazil was a highly under-developed country up until the 1960s — by then, a greater part of the population lived in rural areas, infrastructure in the bigger cities was still poor for most communities, sex education was a complete taboo, and contraceptive methods barely existed. In addition to that, the birth rate in rural communities was especially higher due to the high child mortality rate, which made people have more kids to improve their chances of having one that survives the poor conditions they were exposed to. It was common sense that parents would have more kids, so that some or all of them could help with the land work. This arrangement, however, changed drastically when people started moving to urban areas, had access to healthcare (however basic it was, it was still better than nothing) and birth control methods. Along came family planning, big machines to do the land work, modernization in general, and families started becoming smaller. You can see similar trends affecting other developing countries in the world, although at different times and to different extents. And although the current population is relatively big (~210 million), the trend is pointing towards stagnation in the next few decades. I highly doubt we will see Brazil’s population nearly triple in half a century, as was the case in the 1960–2010 period.
