Large Isospin Asymmetry in ^{22}Si/^{22}O Mirror Gamow-Teller Transitions Reveals the Halo Structure of ^{22}Al

β-delayed one-proton emissions of ^{22}Si, the lightest nucleus with an isospin projection T_{z}=-3, are studied with a silicon array surrounded by high-purity germanium detectors. Properties of β-decay branches and the reduced transition probabilities for the transitions to the low-lying states of ^{22}Al are determined. Compared to the mirror β decay of ^{22}O, the largest value of mirror asymmetry in low-lying states by far, with δ=209(96), is found in the transition to the first 1^{+} excited state. Shell-model calculation with isospin-nonconserving forces, including the T=1, J=2, 3 interaction related to the s_{1/2} orbit that introduces explicitly the isospin-symmetry breaking force and describes the loosely bound nature of the wave functions of the s_{1/2} orbit, can reproduce the observed data well and consistently explain the observation that a large δ value occurs for the first but not for the second 1^{+} excited state of ^{22}Al. Our results, while supporting the proton-halo structure in ^{22}Al, might provide another means to identify halo nuclei.