Ferrocene (Fc) is an effective precursor for the direct synthesis of high quality single-walled carbon nanotubes (SWCNTs) via floating catalyst chemical vapor deposition (FCCVD). However, the formation mechanism of the Fe floating catalyst and the SWNCT growth precursors, such as carbon chains, during Fc decomposition are not well understood. Here, we report first principles nonequilibrium quantum chemical molecular dynamics simulations that investigate the decomposition of Fc during FCCVD. We examine the influence of additional growth precursors including ethylene, methane, CO, and CO2 on the Fc decomposition mechanism and show that the dissociation of these species into C2Hx radicals and C atoms provides the key growth agents for the nucleation of carbon chains from Fc-derived species such as cyclopentadienyl rings. Without an additional growth precursor, Fc decomposes via the spontaneous cleavage of Fe-C and C-H bonds, thereby enabling Fe atoms to cluster and form the floating catalyst. On the basis of these simulations, we detail the two competing chemical pathways present during the initial stages of FCCVD: Fe catalyst nanoparticle growth and carbon chain growth. The latter is accelerated in the presence of the additional growth precursors, with the identity of the precursor determining the nature of the balance between these competing pathways.