It's not it at all.

I don't remember my father ever climbing a single tree, yet I loved it as a kid and was doing it until late teenagehood.

Leading by example is good, but definitely not necessary in all cases.

Maybe your father showed it to you, when you were small and do not remember it.

But yes, it is leading by example. If other kids climb trees, that is an example as well. If "kids these days" rather play on their devices, but I want my kids to experience something different, then yes, I need to show it to them. (But I also, or mainly do it, because it is fun and training for myself).

If we are with other, wilder kids, which we occasional are, no need to show anything to them. But on the default playground today, it really does seems like it has gotten very rare. A tree is not a certified playelement after all and who to sue if something happens, so best to avoid it, is what most probably think.

Now that you mention it, we did have an exercise ladder in my childhood bedroom.

Maybe that's where they taught me how to climb.

Good point. It was the same with me. I climbed trees my entire childhood and never saw my father do it. I doubt my daughter will though as there isn't any forest nearby and in the 90s, kids spent all summer outdoors and that isn't even legal anymore (my parents didn't know where I was for hours at a time when I was as young as 5).

Different people also have different personalities. My brother loved climbing trees. Me? Not at all.

We grown up at the same place with access to the same experiences and trees.

Maybe your kids are just not that into the idea of tree climbing as you were, and maybe this doesn't mean anything about generations?