Tell them (or show them) that you're eating a healthy amount of calories per day, and thus the only thing you're doing different from them is -when- you're taking in those calories.

Maybe you could reason by analogy that if you fill your car with 14 gallons of gasoline once a week, or 2 gallons of gas every day for 7 days, the car has enough fuel. You're doing essentially the same thing with the fuel for your body.

That should assuage any concerns about undernourishment (which are valid concerns to have). If they aren't concerned about undernourishment and are instead objecting "because it's weird" then you're probably never going to be able to reason with them, because they're not using reason themselves. (No offense.)