Well it's based on the theory your metabolism shuts down if you don't eat for long enough. Obviously not true. Also, many people on the sad will have hypoglycemia by then and feel cranky, run down, etc. If you are eating paleo, this shouldn't be an issue. I skip breakfast quite often, with no ill effects.
Breakfast is the first meal of the day with which you "break your fast" after the night.
So technically even if you eat your first meal of the day at 2pm it is still your breakfast. Making that meal a decent one is not a bad thing.
I expect that back in the days when most people worked in hard labour intensive jobs an large early breakfast was much more important. I can't imagine starting a long working day down a coal mine with a pickaxe or harvesting crops in the fields with a sythe on an empty stomach.
There are however many similar food related sayings in the English language. They are repeated through the generations, either they sound good or they just memorable, not because they are correct :)
"An apple a day keeps the doctor away."
"Eat your crusts, it'll make your hair curly."
"Eat your carrots and you'll be able to see in the dark."
"Eat breakfast like a king, lunch like a prince, and dinner like a pauper."
"Man does not live on bread alone."
Just read myth number 7 on Martin's list. This guy knows all there is to know about IFing which is what happens after your last meal of the day. The break-fast will happen at the end of your fast. http://www.leangains.com/2010/10/top-ten-fasting-myths-debunked.html
Actually, some say it's important to eat breakfast if you have adrenal issues, like when they're so tanked they're unable to kick in in the morning. Fasting is suppose to contribute to and perpetuate the problem.
I've recently started skipping breakfast save for a cup of coffee with heavy cream around 10am. Now I eat lunch at about 2-3pm, and dinner around 7-8pm. Never felt better! Much more energized and focused in the mornings.
Before paleo and IF'ing I always emphasized a good hearty breakfast to start the day, especially for my kids. My 12yo won't eat lunch at school so I always make sure they have a solid breakfast - protein, fat, low/moderate carbs. I on the other hand, like to fast until 12-1pm and really have no issues with lack of energy or hunger headaches like I did prior to paleo.
I am not hungry in the morning, so I don't bother. By the time lunch rolls around I am ready to pack it in. I like to eat when I'm hungry. I have come to trust my body to tell me what it needs, and it obviously doesn't need (or want) breakfast.