People who say that "swimming lessons are non-negotiable, I made my children go" do you mind me asking.... what did/would you actually do if your child, despite all cajoling, bribing, persuading etc known to human kind, repeatedly refused to get in the water when you took her to swimming lessons? I was well used to taking dd to activities and indeed school kicking and screaming but she did participate and enjoy it once she was there. Swimming lessons she simply refused to get in.
Having said that, she did swimming lessons at school during KS2 and could swim 25m by the end of Y5. Still not as strong as I'd like her to be, but I can't force her to have swimming lessons. We do go recreationally, although she doesn't really enjoy it.
Similar story with ds, except that his fear was triggered by an instructor taking him down to the deep end on a 'noodle' despite the fact that it was clearly frightening him. (I didn't realise this at the time, as he had his back to me).
At nearly 10, he can just about get himself across a width under water and has, thank god, agreed to have some one to one lessons as he refuses a group.
I learnt to swim by going to some Saturday morning club at the swimming pool when parents left their children for 3 hours with access to the whole of the 25m pool and diving area ('70s!). There was nothing else to do but work out how to swim and I became a strong swimmer very quickly. Never had an actual 'lesson' though.