Chiral singularities in both nucleon isovector radii are calculated in clos
ed form. Within a one-meson-loop approximation we implement in an explicitl
y gauge invariant manner quark substructure in the gamma pi pi and pi NN ve
rtex functions. The coefficients of log m(pi) and m(pi)(-1) terms are direc
tly related to g(A) and to the threshold behaviour of the pi N amplitude A(
(-))(nu, 0) which are 1 and 0, respectively, if only the N pole is consider
ed in the pi N scattering amplitude. This result is remarkably independent
of the cut-off procedure. If mesonic substructure at the gamma pi pi vertex
is included, however, g(A) becomes slightly smaller than 1 and [partial de
rivative/partial derivative nu A((-))(nu, 0)](nu=0) becomes moderately nega
tive. This hints at important contributions to both g(A) and [partial deriv
ative/partial derivative nu A((-))(nu, 0)](nu=0) from the Delta(1232) and p
ossibly other N*, Delta* resonances in this approach.