Websites use black text on a white background because reading is easier on the eyes in that format. The same reason e-readers default to black text on a white background. White text (on a presumably black background) reflects light and scatters onto the other words, thus black text is preferred for
reading.
With MacOS dark mode it's just changing the UI elements and you aren't reading across these elements, but giving subtle glances at the content. Don't think this move to dark mode will change websites, which we primarily read on.
Also, one thing you'll notice is most apps that deliver a dark mode don't use true white text, but soft grey. Most also use a dark (like charcoal) grey background, instead of true black. I'm not in front of my Mac right at this second, but I'm pretty sure Apple is using a soft grey text color in dark mode. Using a soft grey will make text easier to read on the darker backgrounds, because it does not reflect as much light.
All that said, dark mode implemented the way Apple has done it will in theory be easier on the eyes.
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Why would it be more straining on the eyes? The bezels on most Macs are black. You can "replicate" it somewhat, with having a black background, and opening a website with a white background. Do you find it more straining on the eyes?
I am using it right now, and I don't find it straining at all. I've been waiting for a "native" dark mode for years now, so its a really nice addition to Mojave. The only thing that I dislike, is that the Dynamic wallpaper is disabled while in Dark Mode. There also seems to be no transparency on the toolbars (Finder, Safari etc.) while in Dark Mode.
I explained it in the post above, but the OP is looking at this more from a reading perspective than a productivity perspective. From a reading perspective, yes, white text on a black background is harder on the eyes. But reading elements are not the elements that Apple is changing.