"So much for Bill Gates and the Rich"
So, you've thought this through yourself have you, and come to the conclusion that the conspiracy theorists - to whom this is the stuff of their dreams - are right? Bill Gates genuinely wants to use the sinister means described in some of the articles in your Google link to sterilise people, and to kill children by vaccination.
I'm astonished that there are people who actually believe the rubbish that's spouted by writers who can't see further than their own warped prejudices.
Populations have historically increased in countries where vaccination has been introduced, because fewer people died in early life from the common killer diseases of childhood. A growing population isn't the whole story however. What really acts to control world populations over a longer timescale is the live birth rate - the number of babies that are born, and the average world birth rate is declining. If the death rate stays broadly steady, and birth rates continue to decline, the world population will fall in the long term, and in Europe it's happening now - UN predictions show the population of Europe falling by over 100 million by 2050 and by over 200 million by 2150.
The problem is that the fall in birth rates is not evenly spread across world regions - it remains high in the developing countries, and apart from cultural reasons the main cause is a high rate of infant mortality - large numbers of children die, so people try to buffer the effect by having more of them.
Vaccination of children works to reduce the birth rate because it relieves mothers from a good deal of the burden of worry that their children will die in infancy. Add improved education and you empower women; they take more control of what happens to them - they want a better standard of living, and left to themselves they will practice contraception, and birth rates will fall.
Bill Gates knows this, but of course there is no lack of people only too ready to see a sinister motive in what he says. He exposed himself to criticism when he made the vaccination remark, and the genie is out of the bottle - the conspiracy people can have a field day.