It was all a bit more complex in my case. I was never prevented from riding a bike, but I certainly wasn't encouraged as a young teenager.
My dad was a decent amateur time-triallist in the early 1940s. He was called up pretty late and in 1943 went over to Canada for bomber crew training. Over there he had the good fortune to develop what we now call type I diabetes, which of course almost guaranteed that he would survive the war, hence the fact that I'm here now.
He did briefly return to racing but then contracted tuberculosis, ending his cycling days.
I remember him saying once that he blamed much of his later ill-health on his days as an athlete. It didn't occur to me when he said this, but I assume now that he was referring to drugs. If so, his reluctance to introduce me to the world of cycle racing is much easier to understand.
Aged 24, I upgraded to a good quality fast touring bike (Revell Elite). With that I rode solo and unsupported from Bristol to Geneva and back, five days in each direction. This was far beyond anything I'd done before, and I think the demonstration that I clearly had some ability gave my dad a bit of a shock.
I do remember testing myself on a local 10 mile time-trial course, and did well enough to suggest I could have made a go of it. But I was enjoying the style of cycling I was doing - long distances at a comfortable pace - and that is where I stayed. I'd be lying if I said I didn't have some regrets.