I don't quite get this, either.
If the question is about why is distribution symmetrical or not, answer is given
here :
"It accounts for the nuclear coulomb interaction which shifts this distribution toward lower energies because of the coulomb attraction between the daughter nucleus and the emitted electron. (It shifts the distribution upward for positrons.)"
If you were wondering why is there finite "cutoff" at 0
kinetic energy and not finite (in the sense it's zero) at 0 momentum, I don't know. This doesn't make sense...
And if the parent nucleus has zero
momentum in CM frame, how come there is a finite number of electrons with zero kinetic energy ? That should mean that in that case, neutrinos are also having zero kinetic energy (conservation of momentum). Now if there comes up electron with nonzero kin. energy, then neutrino should also have nonzero kin. energy, and sum of energies in this case and in the case where they are both just "standing" is different.