Short answer
Because pink is not produced by any single wavelength. Neither are magenta, brown, grey, white or black. These are non-spectral colours: real, nameable, reproducible colours that exist only as mixtures or as a relationship between a colour and its surroundings, and no amount of splitting light will reveal them.
A spectral colour is one that a single wavelength can produce on its own — the pure reds, oranges, yellows, greens, cyans, blues and violets a prism separates out. Every other colour humans can see requires either a mixture of wavelengths, a reduction in intensity, or a context that changes how the eye interprets it. Since the set of mixtures is enormous and the set of single wavelengths is one-dimensional, the great majority of visible colours are non-spectral.
Magenta is the clearest case. It is what you see when long-wavelength (red) and short-wavelength (blue) light arrive together without much in between. There is no wavelength that does this, because the spectrum is a line: red sits at one end, violet at the other, and nothing lies between them. The visual system, faced with strong long and short responses and a weak middle, produces a colour that closes the loop — which is why colour wheels are circular while the spectrum is not. Pink is the same combination at lower saturation or higher lightness.
Magenta is sometimes called an 'extra-spectral' or 'invented' colour for this reason. It is not an illusion — it is simply not something a prism can show you.
Brown is the most surprising case, because there is a wavelength region that produces orange but none that produces brown. Brown is dark orange — but only when seen against a brighter surround. Isolate a brown patch and surround it with darkness and it appears orange; put it back into a bright context and it becomes brown again. Brown is therefore not just a mixture but a relational colour: it depends on what else is in view, which makes it a direct demonstration that colour is a perception rather than a property.
Violet is spectral, sitting at the short-wavelength end. Purple is not: it is a mixture of red and blue, sitting on the closing side of the colour wheel with magenta. They look similar and the words are used loosely, but they arise differently — which is why a violet in a rainbow and a purple on a screen are not the same kind of colour, and why some violets are notoriously hard to reproduce in print.
Wavelength ranges and perceptual thresholds are given as approximations: both vary between individuals and with viewing conditions, and sources differ on exact boundaries. Where a figure is contested or unavailable, this page says so rather than picking one.