Inner (closed shell) electrons stick close to nucleus so they do not get near to other atoms. The outer (valence) electrons may participate in bonding either by sharing or migrating to the other atom. Electrons which are paired into spin singlets don't bond. If we try to share one of the paired electrons, in a bonding state, with another atom, the electron from the other atom is not antisymmetric with the (other) paired electron. Therefore only the antibonding (or some excited state) will work and binding is unlikely. Unpaired electrons don't have this problem.
. . . first four don't bond!
The strongest bonds come from s and p orbitals (not d,f).