I'll give it one more try.
Think of an individual film frame. It's like a photograph, nothing is moving in it.
Now a scanner is scanning that image. The machine produces a number of horizontal lines (e.g. 480 or 575, or 1080). We'll give those lines a number, starting with 1 or 0, it's not really important. We call the horizontal lines having received an odd number the odd lines, the other ones the even lines.
It doesn't really matter in which order the horizontal lines are produced, because the image isn't moving. When the scanner spot reaches a certain place, it will scan the same "pixel" independent of the sequence of scanning.
The result is a number of horizontal lines, and all we have to do is: make sure we know where each line belongs.
Next step: the horizontal lines are transmitted to another place (through all sorts of in-betweens). It could be done in various ways, but two specific orders of transmission are really standardized: interleaved (all odd lines first, then all even lines), or progressive (all lines directly after each other).
Top to bottom.
Now they are sent to a display, to be shown to the human eye. All that matters is: they should get at the proper place.
This can be done in various ways too: older TV sets, for instance, presented each "odd half-frame" after each "even half-frame" (each horizontal line exactly at the right place!) and let the human eye do the cumulating.
Why? Because the frame frequency was too low, and progressive images would result in visible and distracting flicker (the top of the image was fading out already before the bottom was painted on the TV screen).
More modern monitors present the image at a much higher frame-rate (~ 100Hz). CRT-type displays still have to "paint" their image (top-down), but LCD- and Plasma-screens don't have to do that. Those images are read from a cache memory.
Now all that matters is: the various horizontal lines have to get at their right place inside the image. If they do, the image is "perfect" (for the given resolution). Jaggies and moiré may be there, but will not be caused by the way the horizontal lines were transmitted.
If you want to call the resulting image of an LCD-screen "deinterlaced", you're free to do so, but then the term has become worthless, since the real difference is the way the lines were transported.
Once the image is reconstructed, it's no longer possible to tell how (in what order) it was transmitted.
Note that I do not try to muddy this topic with problems around 3:2 pull down (NTSC) and that we're explicitly not discussing real time moving images (TV and video recorder).
Interleaved vs. progressive, apples to apples.