Viktor Toth’s answer correctly describes how our current theory is constructed so as to have the kind of symmetry that leads to three quarks being required to make a proton, but says nothing about why the theory had to be constructed that way and even less about why physics should actually follow such a theory. The first question (of why our theory had to be built that way) is answered by looking at various patterns of relationships between the scattering cross sections for different interaction and decay processes of elementary particles (though the details are beyond my capacity to explain in a Quora answer). But the second question (of why physics actually is that way) is, so far as I am aware, something that no-one yet has an answer to. (It may turn out that the number three is for some reason the only one consistent with some more fundamental properties that we think physics should have, but I have not yet seen any such argument.)