I am having trouble wrapping my head around this. Can you explain like I'm 5 yrs old, or is there somewhere I can read further on this? Specifically I don't understand the justification for dividing the pitch by 2, just because there are 2 lines?
The technicalities (which I lazily didn't go into - or as I like to tell myself, for reasons of simplicity) are that resolution (perceptibility) is measured using "line pairs". In other words, dark, light, dark (or light, dark, light - but there are complicating factors with this). The limiting resolution is when the two lines no longer look like two lines, but merge into 1.
The justification is that when analysing resolution as a frequency (as is normal in scientific work), you measure the frequency by the distance between 2 transitions - this is for consistency with the normal way of measuring frequency: if you have a sine wave, 1 cycle is the distance from crest-to-crest; in other words, crest, trough, crest.
The other issue is that, you need 2 pixles per line pair (in the limiting case of a striped pattern).
The final issue raised, that of vernier acuity is (I think) a bit of a red herring. Vernier acuity refers to the fact that humans can detect a "step" in a line which is smaller than the resolution that they can see; for example, if the smallest line pair a person can detect is 0.6 arc minutes, then they could still tell if a line is "stepped" if the step is only 0.1 arc minutes.
If you look at a line that has been rendered with anti-aliasing, you might see that it is 2 pixels wide, but one pixel is brighter than the other. If the line is at co-ordinate 5.3; then you might see pixel 5 show 70% of the line's color, and pixel 6 show 30% of the line's color.
Vernier acuity works, because the brain can reverse the anti-aliasing process to estimate the position of the line. Because this is already an algorithmic process, it still works, even if the image of the stepped line is artificially blurred. So, as long as you have accurate anti-aliased rendering, you don't actually need your screen to have 10x the resolution to get this effect.