Energy of activation vs Bond energy
The bond dissociation energy is the energy needed for the reaction leading to the rupture the $\ce{C-H}$ bond. I.e. it is the enthalpy of the reaction:

$$\ce{CH_3-H \rightarrow CH_3^{\bullet} + H^{\bullet}}$$

In the case of the reaction in the question, formation of the $\ce{H-Cl}$ bond will counterbalance the energy cost for breaking the $\ce{C-H}$ bond.