I am not a father, but what I observe works best if the father (or mother) takes the hobby himself first. Kids really seem to be motivated to learn from parents, but you need to let them come to you, instead of you forcing them to learn something you are not interested doing yourself (even in small doses).
I'm a father and you're spot on. It's easy to project what you would like children to get into and just tell them to try it, but it's essential to show that you're into it as well (even -- and especially -- if you're not!)
Maybe you lack imagination.. I can think of a lot of things more discouraging than that.
If only I had had anyone in my extended family familiar with computers when I was a teenager.
But I'm not sure about programming before the age of ~13 or whenever something like algebra shows up in school.
12 year old me would have greatly appreciated it. Instead I had to wait until college to get exposed to actual programming lessons and assignments.
My experience was much different from yours then. I taught myself programming and when I got to college I found I was learning nothing new (in terms of practical software development) and dropped out after two years. Never looked back
"I'm going to need you to attach estimates to your JIRA tickets and join the scrum at 8:15, son"