  Millisecond pulsars (MSPs) and normal non-recycled pulsars are both detected
in $\gamma$-rays. However, it appears that a much larger fraction of known
energetic and nearby MSPs are detected in $\gamma$-rays, in comparison with
normal pulsars, thereby making undetected $\gamma$-ray MSPs exceptions. In this
paper, we demonstrate that the viewing angles (i.e. between the pulsar spin
axis and the line of sight) are well described by the orbital inclination
angles which, for binary MSPs with helium white dwarf companions, can be
determined using the relationship between the orbital period and the white
dwarf mass. We use the predicted viewing angles, in complement with values
obtained from other constraints when available, to identify the causes of
non-detection of energetic and nearby MSPs from the point of view of beaming
geometry and orientation. We find evidence for slightly different viewing angle
distributions, and postulate that energetic and nearby MSPs are mainly
undetected in $\gamma$-rays simply because they are seen under unfavourable
(i.e. small) viewing angles. We finally discuss the magnetic fields of
$\gamma$-ray detected pulsars and show that pulsars which are efficient at
converting their rotational energy into $\gamma$-ray emission may have
overestimated dipolar magnetic field strengths.
