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X-shaped radio galaxies (XRGs) produce misaligned X-shaped jet pairs and make up $\lesssim10\%$ of radio galaxies. XRGs are thought to emerge in galaxies featuring a binary supermassive black hole ($\rm SMBH$), $\rm SMBH$ merger, or large-scale ambient medium asymmetry. We demonstrate that XRG morphology can naturally form without such special, preexisting conditions. Our 3D general-relativistic magnetohydrodynamic (GRMHD) simulation for the first time follows magnetized rotating gas from outside the $\rm SMBH$ sphere of influence of radius $R_{\rm B}$ to the $\rm SMBH$ of gravitational radius $R_{\rm g}$, at the largest scale separation $R_{\rm B}/R_{\rm g} = 10^3$ to date. Initially, our axisymmetric system of constant-density hot gas contains weak vertical magnetic field and rotates in an equatorial plane of a rapidly spinning $\rm SMBH$. We seed the gas with small-scale $2\%$-level pressure perturbations. Infalling gas forms an accretion disk, and the $\rm SMBH$ launches relativistically-magnetized collimated jets reaching well outside $R_{\rm B}$. Under the pressure of the infalling gas, the jets intermittently turn on and off, erratically wobble, and inflate pairs of cavities in different directions, resembling an X-shaped jet morphology. Synthetic X-ray images reveal multiple pairs of jet-powered shocks and cavities. Large-scale magnetic flux accumulates on the $\rm SMBH$, becomes dynamically important, and leads to a magnetically arrested disk state. The $\rm SMBH$ accretes at $2\%$ of the Bondi rate ($\dot{M}\simeq2.4\times10^{-3}M_{\odot}\,{\rm yr}^{-1}$ for M87*), and launches twin jets at $\eta=150\%$ efficiency. These jets are powerful enough ($P_{\rm jets}\simeq2\times10^{44}\,{\rm erg\,s}^{-1}$) to escape along the spin axis and end the short-lived jets state whose transient nature can account for the rarity of XRGs, Comment: 10 pages, 4 figures