Huh, I have vague memories of swimming lessons being a compulsory part of my primary school education. Maybe this was a product of the school being within walking distance of a pool and not a universal fact of life. In practise though I have been able to swim for sufficiently long that I don't remember the process of acquiring the skill any more than I remember learning to walk. I guess that's evidence for "most people learn as a small child", then?

(I used to swim a lot because it was exercise I could do on my bad leg and I miss it a bit but it's kinda really inefficient in terms of the time-costs getting to and from anywhere I could swim)