An adult who apologizes to a kid is an adult with nothing to prove.

Apologizing down the age gap is optional in a way that apologizing sideways is not. Plenty of adults avoid it, on the theory that authority depends on never being wrong. The ones who do it anyway are demonstrating that their standing does not rest on being right. It also teaches whoever is watching that admitting a mistake is survivable.

Notice which adults in your life can do it, since those are the ones to go to when you have made a mess. And apply it downwards yourself, to a younger sibling or a kid you coach. Saying sorry to somebody who cannot make you is where this starts.