I have come very late to this thread due to end of semester grading and
such. But it seems to me that people may be failing to distinguish
between the contact force that causes friction and the frictional force
itself. You have to have a force pushing to surfaces in contact to
generate a frictional force. The contact force is not the same as the
frictional force.
Static friction only comes into play when there is another force
PARALLEL to the surface which, in the absence of friction, would cause
sliding to take place. The friction then will exactly oppose that force
parallel to the interface of the two surfaces, up to a limit controlled
by the contact force and the coefficient of friction.
The frictional force prevents your feet from sliding, but the contact
force accelerates you. Obviously you could not move your center of mass
without a force from the outside.