Ullmann's Reaction (similar to Wurtz) - aryl chloride with deactivating groups - stability of free radical
Your assumption that electron-withdrawing groups destabilize radicals is wrong. Radicals are in fact stabilized by both electron-withdrawing and electron-donating groups and even more so if both types are attached to the same carbon atom (captodative effect).

I modified an image from Ian Fleming's Molecular Orbitals where you have the proof. In the image you can see that the combination of the carbonyl group's (which is electron-withdrawing) pi bonding/antibonding pair of orbitals with the p orbital of the radical results in an overall decrease in energy: