You are forgetting two important reasons why population was able to grow so incredibly last century: modern medicine and agriculture.
Never before the modern petrol-based industrial economy were we able to treat disease so effectively or grow so much food. That's why the population did not explode thousands of years ago. Human society simply did not have the tools to support billions of people. Prior to 1900 (and often prior to 1950) the world was not blessed to have things like food refrigeration, plastics, antibiotics, tractors and mechanical harvesting equipment, safe food-preservation methods, or country-spanning highways for trucks to distribute and deliver everything else I just mentioned. It took a long time for humans to learn this stuff.