Something about momentum? I’ll bet, because if an object is already falling, in temperature, presumably, it should require extra time and effort to turn it around and make it rise. You first have to kill its downward momentum.
That’s all very well and true for physical objects, but temperature isn’t a physical object. When the weather report says that the temperature is falling, we hardly expect to hear a crash.
Temperature is just our artificial human way of expressing the average speed of the molecules in a substance, because their speed is what makes a substance hot; the faster its molecules are moving, the hotter it is. We can’t get in there and clock the speed of every single molecule, so we invented the concept of temperature. It’s really little more than a handy number.
In a pot of warm water, the zillions of molecules are flitting about at a higher average speed than
in a pot of cold water. Our job in heating the pot is to give more energy to those molecules and make them move even faster, eventually fast enough to boil off. Obviously, then, warm molecules will require less added energy than cold ones, because they’re already partway to the finish line: the boiling point. So the warm water will boil first.
And you can tell him I said so.
Using hot tap water for cooking may be unwise for another reason. Older houses may have copper water pipes that are joined with lead-containing solder. Hot water can leach out tiny amounts of lead, which is a cumulative poison. So it’s a good idea always to use cold water to cook with.
Yes, it’ll take longer to boil, but since you may live longer you can spare the time.