Cooking has health benefits
If you cook, you control what goes in your food. That's reason enough to do it.
As for all the bad things in food that isn't prepared by you or your family, I recommend the book Salt Sugar and Fat. It describes how the processed food industry, and to a smaller extent restaurants, make choices that are good for business, good for taste, and bad for your health.
Cooking your own food allows for better control of what is ingested, a lesson that should be cultivated in children as early as possible. It also serves as a mechanism for avoiding excesses. For example, making your own french fries reduces the amount of french fries consumed, because of all the trouble it is to make them at home, from scratch, and clean up afterwards.
Cooking is educational
It's a great way to introduce science. Physics, chemistry, arithmetic, measuring, biology, nutrition (duh). Something as simple as making a vinaigrette illustrates different densities (vinegar and oil), solutions (salt in vinegar), immiscible liquids, emulsifiers (mustard), the importance of measuring quantities , acids (vinegar), fats (lipids), salts.
Cooking teaches production engineering. (Well, it is production engineering. Think about it.) Planning, organizing, executing, measuring, controlling, failing and recovering (when in doubt add butter), scaling recipes up and down, dealing with spoilage and leftovers, balancing choices (making baklava takes a lot of time, but sometimes you really want baklava). It can also be used to bring up the matters of cost management. Never too soon to teach kids fiscal prudence.
Cooking creates opportunities to talk about history, culture, and geography. Yes, food itself could be used to introduce these topics, but if you do it in the preparation (and the purchasing) it will be better remembered, and it fills up the time when things are in the oven or fermenting.
(As a side benefit, cooking also educates the parents, as they need to be prepared for teaching the children.)
Cooking develops important traits
Discipline. Like most interactions with the real world, cooking utensils and ingredients are very hard to emotionally blackmail or bargain with.
Patience, carefulness, study habits, observation skills. Because there's a clear payoff at the end, the food, cooking can be used to develop these important life skills. Baking and sauce reductions, for example, teach patience and carefulness. Analyzing recipes and procuring fresh ingredients develop study habits and observation skills.
Plan, Prepare, Work, Clean-up. Many intellectual experiences or intellectual descriptions of physical experiences are too circumscribed. Cooking provides a teaching laboratory for thinking about interaction with the real world: plan the work (and the shopping trip); organize the resources into a mise-en-place; do the work (this is the part that matches most intellectual tasks, the carefully circumscribed activity); clean-up and deal with the consequences.
Rule-following and creativity in balance. This is a very important life lesson, that many people get wrong. There are times when following the rules (the recipe) is essential, especially for beginners. And there are times, usually after a long period of following the recipes so that their rationale is well understood, for deviating and being creative. Creativity is not randomness borne of ignorance, it's willful deviation from rules borne of deep understanding of those rules.
Respect for manual work. Many educated people have a latent bigotry against manual work. Cooking, by integrating the intellectual, the creative, and a lot of physical work, acts as prophylaxis against that bigotry. (Lifting weights and playing a musical instrument partially remove this bigotry as well.)
Cooking is a bonding experience
Humans are, or so I'm told, social animals; apparently, you people like to do things in groups. Cooking presents many opportunities to develop teamwork and leadership skills. And it's extremely meritocratic, as the taste of food doesn't depend on the personal characteristics of those preparing it, other than through the actual cooking.
Family time is good, shared family work much better. Cooperating towards a shared goal creates a stronger bond than just spending time together. Teaching your children to cook is an act of love. It's a lot of work, of course, but that's part of the whole "love" thing.
Cooking has physicality
When things are done in the real world, there's no 'preferences' panel, no 'undo' button. Interacting with physical objects teaches important lessons about reality in a way that no intellectual task (reading, watching, simulating on digital devices) can: things smell, break, are hot, sharp, sticky; sauces separate, soufflés deflate, meat burns, vegetables wilt, frozen desserts melt, cakes crumble, liquids spill.
Also, for small children, cooking provides both opportunity and motivation for developing dexterity and sensory skills. Dragging a finger across the screen of an iPad is not adequate activity to develop motor skills and there are more senses than vision and audition.
Cooking is an important skill to have
Even if all the above benefits were unimportant, which they aren't, cooking is an important skill to have.
You don't have to be a prepper to understand the value of being able to turn ingredients into a meal; you don't have to be a food critic (better yet, a gourmet) to appreciate that a little bit of knowledge about flavor creation and combination can make a lot of difference; and you don't have to be an hypochondriac control freak to be suspicious of the quality of ready-to-eat meals.
Most of all, cooking has a smooth learning curve which makes it one of the easier skills to acquire and maintain, and the results are often delicious and almost always edible.
Cook and teach your children to cook.
