Quantum calculations with the density functional theory (B3LYP) have been carried out to compare the reactivity of aryl-H and aryl-F bonds toward oxidative addition and to understand the high degree of inertness of the latter. The thermodynamic energy patterns for oxidative addition of 1,4-difluorobenzene toward two very different metal fragments have been examined. In one of them the final product of oxidative addition could be a 16-electron unsaturated complex of the type Os(H)(CO)(C6F2H3)(PH3)(2) and/or Os(F)(CO)(C6FH4)(PH3)(2). In the other system the final product of oxidative addition could be an 18-electron saturated complex CpRh(PH3)(H)(C6F2H3) or CpRh(PH3)(F)(C6FH4). These two systems are models for experimental complexes which prefer the C-H to the C-F oxidative addition. The calculations reveal that, for both systems, the C-F oxidative addition is thermodynamically preferred, especially in the 16-electron case. The activation energy has been determined in the case of Rh, and it is shown that the activation energy for C-F activation is considerably higher than that for C-H activation. This clearly shows that the inertness of the C-F bond has a kinetic origin.