If you use purified/distilled deionized water, nothing will happen if you reboil it. Ordinary water, however, contains dissolved gases and minerals. The chemistry of water changes when you boil it. Boiling water "drives off the volatile compounds and dissolved gases."
If you boil water too long or reboil it, certain undesirable chemicals can become more concentrated. Examples of such chemicals include nitrates, arsenic, and fluoride.
There is a concern reboiled water can lead to cancer. This concern is not unfounded. Boiled water is fine. But increasing the concentration of certain toxic substances can cause illness, including cancer. "For example, excessive intake of nitrates has been linked to methemoglobinemia and certain types of cancer." Arsenic concentration and exposure may produce symptoms of arsenic toxicity plus it has been associated with certain forms of cancer. Even healthy minerals can become concentrated to dangerous levels. A common example is calcium salt. Concentrated levels of this mineral (excessive intake) can lead to things like kidney stones, hardening of the arteries, arthritis, and gallstones!
So here's the bottom line, Cooling it down and then reboiling it doesn't present a concern or health risk. Some humans leave a teapot on the stove and just keep adding water to it as they need to. By adding fresh water to the kettle and then reheating it, won't likely endanger your health. It's best, however, if you don't let the water boil down first, though. This practice can concentrate those dangerous minerals and gases if you reboil it. If you do reboil water, it best to do it only once or twice and not make it your standard practice.
Little Quigley learned a valuable lesson. He now knows that it's best to start off with a fresh pan of water. And I'm happy to say, that our brotherly Mother's Day lunch went off without a hitch.
Many humans aren't aware of the Do Not Reboil rule. If you're one of them, I hope you found this blog helpful and useful.
Until tomorrow, I wish you all