I also very much dispute the oft-cited claim that "breakfast is the most important meal of the day" - my theory is that it came about as a marketing push for breakfast cereal companies looking to push their cheap carbs. It's become an ingrained, indisputable "truth" - hence some of the comments you got.
I remember being told as a kid that breakfast was really important, so I had "energy" and would be able to concentrate better.
I realise now that it's nonsense, at least if you eat a carb-laden breakfast. Eating carbs seems to start a cycle where you are going to feel hungry ~2h after eating (signalled by a blood sugar drop back to normal levels), regardless of how much you ate. I remember this from my school days too, not being able to focus because all I could think about was my next snack/meal!