I suppose there's a bit of it in my family. My grandfather always had a large garden. Bigger then what I have. I always remember pulling a carrot, wiping it on my shirt, and eating it. They were always my favorite. Washing them in the sink seemed to ruin the taste. And they tasted better then store carrots.
I grew up in NH and there were always blackberries growing wild in the woods. Or raspberries. Eating them always seemed like you were getting away with something.
My mom always had an herb garden. I ate lots of chives. Later she grew green beans, summer squash, potato, cabbage, asparagus.
My aunt has had a garden that dwarfs the one my grandfather had. My uncle has a garden and another aunt has had sheep, goats, chickens and a llama.
So there's some family history there.
Now, I see my kids eating things. Chives are ready (in small bits) right now n the back yard. There's mint. I can usually pull some celery off for them or the neighbor kids. My daughter loves tomatos and helps pick them. Well, she picks them from the basket after I put them there and then she eats them. She's getting away with.. something. And later in the season, we'll harvest her next favorite, Brussels Sprouts.
Garden vegetables taste better so its easier to like them. I know how they're grown, what chemicals went into them (none!) and what's in the soil.
It's fun to see them appear, ready to be eaten. With the zucchini, we can get 3-4 a day when they produce. It's fun to give them to neighbors and friends.
We have deer, fox, birds, hawks, kites, woodpeckers, squirrels, woodchucks, fischer cats (but they don't eat woodchuck :-( ) and rabbits. I've seen a few cucumbers with rabbit marks, lost a whole tree of peaches to the deer or woodchuck (I'm working on fixing that this year) but it's worth it to see them in the backyard. Well, maybe not the peaches. I've heard woodchuck is good eating.
There are some moral and philosophical reasons as well. Organic, localvore, sustainability, back to nature, survivalist, generalist, maker, experimenter, naturalist kinda things. I've always believed that everyone should be able to prepare a meal for themselves. Cook it, grill it, even pour a bowl of cereal. It's always good to learn how to make. I've brewed my own beer, baked bread, gone fishing, eaten wild animals and wild plants, made things out of wood, metal and done crafty things. Growing plants to eat is right up there with all of that.
Saving $$$ isn't one of my reasons. I'm not sure it costs any less then buying "organic" at the store. I've bought fencing, tools, watering equipment and whatnot. I've got lights and heat to start seedlings. That will probably break even compared to buying transplants. Luckily my wife isn't overly concerned about landscaping or that would add more costs.
We enjoy the back yard more. It's not a sterile lawn anymore. We watch the kids, work on the garden project(s), and see the ecosystem at work.
The homebrewing (beer) movement has a saying: Relax, don't worry and have a homebrew. I think gardening is like that.