Re: Other writing
The best contraceptive seems - across the years - to be education. Simple but broad education helps people to "better themselves" (not a fan of that term, but it conveys a meaning), and people who are more secure feel less need for the large families - for plenty of children to help scratch a living from the land, to bring in dowries on marriage, to look after you when you are old. It's not as if varied methods of birth control aren't available worldwide, it's that without education people don't necessarily understand the benefits.
On a very crude level, a woman who is educated - especially if she has a job - will almost always delay starting a family. Having your first child later means less opportunity to produce children.
It's a very complicated subject and just providing the method of control doesn't work so well without the other things.
I'm probably utterly misrepresenting the man, but the impression I got wasn't one of suggesting birth control as a way of helping the poor of the third world out of poverty, per se, it was more a colonial "look at these savages who aren't as sophisticated as us, let's teach them cricket".
Eugenics was still "a thing" in the 1950s and 1960s and only really started fading out in the 1970s, even among people who were otherwise incredibly progressive. I know a person who spent the best part of their life improving the lives of those with what used to be termed "mental handicaps", treating them as people with skills to offer society, and not as sub-human anomalies deserving of a life locked up in an asylum, and yet this person still to this day would argue for - if you asked - sterilisation of such people and would advise abortion if a diagnosis was made prenatally.
<aside>I had quite shocking personal experience of this when one of my own children was born with a medical condition needing quite a lot of hospital treatment, but which was not at all life-threatening or -limiting and certainly had no bearing on mental acuities. One of my (admittedly elderly) relatives' first reaction wasn't "congratulations on your new baby" but "oh dear, I am sorry", and for the next fifteen years or so conversations often started along the lines of "how is poor x these days?"</aside>
It's only one step from there (sterilisation) (and thankfully it's a step that person doesn't take) to argue that children growing up in certain "sink estates" should have long term contraceptives fitted by default, so that they don't become parents as soon as they leave school.
Suggesting that birth control is "the answer" sees "overpopulation" as a singular problem, and doesn't understand that "lifestyle" is a large part of it. I have no evidence to back this up (look up those regular "how many planets" articles) but it's entirely possible that a family of two grandparents, two parents and six children living a simple but productive life in one of the poorer parts of the globe actually has a small fraction of the environmental impact that a 2+2 family has in the western world. The planet could probably support more people overall if we in the west reduced our use of its resources, even if people in the poorer parts started using more.
Population rise in the "western world" is an interesting thing. It is absolutely not happening because of the birth rate. In the UK, for example, the average fertility rate in 2018 (children in each "completed family") is 1.89 children, with the total fertility rate (see the source) now at 1.70 per woman - and it has been below 2.0 (the crude replacement rate) since the mid 1970s.
Maybe I'm overthinking it. I certainly don't have the answers, and as a westerner I'm part of the problem.