We present quantum chemical simulations demonstrating how single-walled carbon nanotubes (SWCNTs) form, or "nucleate", on the surface of Al2O3 nanoparticles during chemical vapor deposition (CVD) using CH4. SWCNT nucleation proceeds via the formation of extended polyyne chains that only interact with the catalyst surface at one or both ends. Consequently, SWCNT nucleation is not a surface-mediated process. We demonstrate that this unusual nucleation sequence is due to two factors. First, the pi interaction between graphitic carbon and Al2O3 is extremely weak, such that graphitic carbon is expected to desorb at typical CVD temperatures. Second, hydrogen present at the catalyst surface actively passivates dangling carbon bonds, preventing a surface-mediated nucleation mechanism. The simulations reveal hydrogen's reactive chemical pathways during SWCNT nucleation and that the manner in which SWCNTs form on Al2O3 is fundamentally different from that observed using "traditional" transition metal catalysts.