There was an experiment done in the early 70s that took a bunch of school children who all normally chose to eat breakfast, deprived them of it for several weeks, and documented the plummet in their school performance. On the basis of that, a lot of schools implemented voluntary lunch programs (voluntary in that students don’t have to participate). It helped a lot of kids, because the sort of kids who were eligible for free breakfasts were kids who didn’t always get a good dinner the night before, and kids who took advantage of the breakfast but paid, were kids who wanted to eat breakfast, but came from families with two working parents, who were often rushed in the morning. Going to school a little earlier and eating there benefited those kids.
However, about 20 years after the initial experiment, someone finally did a follow-up, where they divided kids into two groups based on whether they freely elected to eat breakfast or not, and tried to match them on other factors, like the general availability of good food in the home, whether the family ate dinner together, how often they had homemade meals vs. take out, etc., and found no difference in school performance.
So, clearly, if a kid wants breakfast, it is highly beneficial to the child to give them breakfast, but if he doesn’t, a morning battle over whether or not he will eat it isn’t necessary.
My son is a non-breakfast eater, although sometimes he will eat a small bowl of cereal or a piece of fruit. My only rule is that he has to drink a glass of milk, at a minimum, in the morning, and that’s because he is really big for his age, and I want to make sure he gets enough protein. He doesn’t mind that, because he likes to have something to drink, and will have some water or juice as well, usually. If we have watermelon, he likes that in the morning. He sweats a lot at night.
I eat breakfast, but I skip lunch a lot. I’m on my own schedule. When I’m working in an office, I eat three meals, or I tend to get hungry at inconvenient times.