It's a mathematical trick. The guitar string is not a sum or superposition of "substrings" vibrating at different frequencies with different amplitudes. You can *approximate* the string's behavior with Fourier or other mathematical analysis techniques ... but the string does what it does independent of your analysis!Then my question is: if you "mute" all the harmonics except for those having a node at that particular point, it means that they really do exist and that they're not just a mathematical trick.
Many moons ago, when I was a young student filled with mathematical techniques, I built a circuit that produced a square wave. When I slapped a scope on it, I somewhat expected to see harmonics in the output ... but the output simply went up and down, with some ringing on the transitions. The ringing was intrinsic to the circuit itself and not actually in the input. That really got me thinking about a how a narrow bandpass filter really works. You think of it "extracting" a signal from the input but it's actually a pseudo-oscillator responding to the input, i.e. it doesn't "extract" anything.
The next step is to wonder whether superposition is ever "real"...