It's just a (most likely approximate) observational fact of nature, how the weak interaction (or rather the electroweak interaction) couples the fundamental particles (quarks, leptons, and the Higgs boson) through the appropriate gauge fields.
Historically the description of the weak interaction started with Fermi's QFT model for ##\beta## decay. Later on there was a lot of experimental confusion about the details of the interaction, and thus Feynman and Gell-Mann wrote down the most general model for couplings of the leptons and after some great experimental effort, including the discovery of (maximal) parity violation through the em. interaction, the entire story ended up with the discovery that the weak interaction is mediated by the current pattern ##V-A## (vector minus axial vector currents).
The trouble with these Fermi-like four-fermion point coupling models however was that they were not renormalizable. After the discovery of the non-Abelian gauge theories the idea came up that there should be a gauge theory for the electroweak interaction. At the same time the weak interaction is very short-ranged and the physicists thought there must be massive gauge bosons for describing such short-ranged interactions if mediated by gauge bosons. Unfortunately a naive mass term kills gauge invariance and spoils the consistency of the entire gauge model (violating unitarity besides all kinds of nasty artifacts).
Then there was quite some theoretical confusion, because what was clear through the work of Nambu, Weinberg et al. concerning spontaneous symmetry breaking, one can have chiral models with massive particles when the chiral symmetry is broken. Now the misunderstanding for a while was that this was thought to imply the existence of massless scalar or pseudoscalar bosons (Nambu-Goldstone modes), and no such thing was wanted in connection with the weak interactions.
However, and this is important, and as Anderson first figured out, the Nambu-Goldstone modes only occur in the physical spectrum where the spontaneously broken symmetry is global. As soon as you gauge the symmetry, i.e., make it a local symmetry, by introduction of the corresponding gauge bosons, the would-be-Nambu-Goldstone modes can be absorbed into the gauge fields by a clever choice of gauge (the socalled unitary gauge). Then the gauge bosons "eat" the Nambu Goldstone modes giving them a third polarization degree of freedom and make them massive without breaking the gauge symmetry at all (in fact, you cannot spontaneously break a local gauge symmetry according to Elitzur's theorem).
Then Higgs figured out that nevertheless, if you want a (superficially) renormalizable theory, there'll be always at least one massive scalar boson in the theory, the famous Higgs boson.
What was also unclear for a while was whether non-Abelian "Higgsed" gauge models are really renormalizable. The trouble is that in the unitary gauge it's not manifestly renormalizable. The trick was to introduce another gauge and a gauge-invariant renormalization scheme by 't Hooft and Veltman, i.e., the socalled ##R_{\xi}## gauges and dimensional regularization. In the ##R_{\xi}## gauge you apparently reintroduce the would-be-Nambu-Goldstone modes, but as it turns out together with the Faddeev Popov ghosts you need anyway to quantize the gauge theory properly, they just compensate unphysical degrees of freedom in the description of the S-matrix, i.e., at the end you get a unitary S-matrix with only physical degrees of freedom (in the usual perturbative sense of course).
The very exciting history of how the Standard Model was discovered in a very illustrative example for how model building works as a process involving both theory and experiment, see
F. Close, The Infinity Puzzle