Not nearly as important as food; the only thing as important as the food supply is our supply of drinking water. Nothing else is comparably important, so you're wasting your time trying to find analogies. And the instability historically see in the oil industry is precisely what sane people want to avoid in the food supply.
Guess what modern agriculture (tractors, fertilizers, pesticides) runs off of?
Furthermore, if food security really is important, why is only dairy and egg supply managed? Surely if you want to keep your country fed, you'd want to go after the staples like potatoes or grain? If all the milk cows and egg laying chickens vanished, people would have to change their eating habits. Some people (working in adjacent industries) might lose their jobs, but that'd be it. On the other hand, if all the wheat/soybean/corn/rice/potato crops vanished there would be a massive famine.
Canada is extremely competitive on grain and potatoes (and lentils and oilseeds and ...). Supply management isn't needed if we're already competitive exporters of a given product.
sounds more like the real goal is protectionism rather than "having a stable supply of food"