I think the comment was more about phases of the day. Like for example, your phone might come pre-installed with a sleep mode from 23:00 to 06:00, which roughly fits for most users. Should we use UTC everywhere, then you'd have to have different presets for different parts of the globe.

Or say you wake up just a bit after sunrise at 7am everyday and you fly across the continent for vacation. Now you have to change all your alarms because sunrise is suddenly at 3am.

Or what if you're writing a book and you want to tell the reader what time it is: 15:00 will mean something else to readers around the world. And while you could attempt to cover it up with "15:00 in the afternoon", there will still be a disconnect between your words/intentions and what the reader pictures.

UTC would be a bliss for programming and scheduling events in this funny little globalized world, but as animals we still base our days on the burning fireball in the sky and removing that connotation from our timekeeping messes with linguistics and clear communication.

I don't think the system we have is perfect either, but I don't think employing UTC everywhere is the way and I don't have other suggestion either.