The complementary color, and the version that works

Because hue-rotate is a fixed 3×3 matrix, not a trip through a color wheel. Filter Effects Module 1 defines the shorthand as a linear approximation applied to gamma-encoded sRGB, and a linear operation cannot preserve saturation while turning hue, so the result drifts. Feed it pure red and it returns #006d6d, a muted teal, where the wheel opposite of #ff0000 is #00ffff — the hue is roughly right and roughly two thirds of the saturation has gone. Use the filter when you are genuinely applying a filter to a whole element, and use a computed value when you need a color.

Your visual system has no luminance boundary to lock onto, so it never settles. Edge detection in early vision runs almost entirely on luminance, and when two hues happen to sit at nearly the same relative luminance the boundary between them exists only in the chromatic channels, which resolve far less sharply. On top of that the lens refracts short and long wavelengths to slightly different depths, so a saturated blue on a saturated red appears to sit at a different distance — an effect called chromostereopsis. Neither problem is caused by the colors being opposite; both are caused by their luminance matching, which is why the fix is a lightness change and not a hue change.

A split complement keeps the tension and drops the confrontation. Instead of one partner at 180° you take the two hues flanking it, conventionally at 150° and 210°, which gives you a three-color set where nothing is anybody's exact opposite. Nothing sits at the point of maximum hue conflict, so the set tolerates being used at larger areas than a true pair does, and the two flanking hues are close enough to each other to act as one family with the base as the outsider.

The HSL flip, unless you have a reason to want one of the others. It is what every other tool and every design handbook means by the word, so a hex from it will match what a colleague gets elsewhere. Reach for the LCH opposite when both colors have to feel equally strong — it holds perceived lightness and colorfulness constant, so neither side wins by accident — and reach for the filter value only when you are literally writing a hue-rotate rule and need to know what will come out.

Because an afterimage is a fatigue effect in the retina and a wheel opposite is a piece of geometry. Stare at a saturated patch and the cone types responding to it adapt downward, so when you look away the opponent channels rebound and you see something in the vicinity of the complement — but the amount of rebound depends on how long you stared, on how bright the room is and on which cones were loaded. Nothing about that process is committed to landing 180° from where you started, so the two agree in family and disagree in the digits.

No, and the tool will hand you the same grey back. Hue is undefined at saturation 0 — every hue produces the same pixel — so rotating it by 180° is arithmetic on a number that does not describe anything, and #808080 flips to #808080. If a near-grey is what you have, the interesting question is usually which hue it is nearly, and a color with even 3% saturation will flip to a visibly different near-grey.

Yes — the hue is untouched. The rebalanced swatch keeps the same angle on the wheel and moves only along the two axes that carry no hue information: lightness, pushed away from the base half a step at a time until the pair reaches 4.5:1, and chroma, cut to 65% so the two are not competing at equal intensity. Anyone checking your work by rotating the hue of the base will land on the same family; they will just find you had an opinion about how much of it to use.