Why does increasing altitude (low air pressure) results in lower resistivity/ breakdown voltage?

The behaviour is described by Paschen's Law.

Electrons are accelerated in the electric field between two electrodes. If there are gas molecules in the path of the electron it will collide with them with a certain probability and it transfers some of the energy to the molecule.
The longer the statistical distance between two collisions is, the longer the electron can be accelerated in the electric field. Only when the electron reaches enough energy to ionize the molecule an arc can be produced.
Lower air pressure -> less collisions -> Longer acceleration and more energy in the electrons for ionization.
At some point the pressure reaches almost a vacuum, then the breakdown voltage starts to increase again, because the electrons don't hit any molecules they could ionize.

You probably ought to look up Paschen's law: -

Paschen's law is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length. It is named after Friedrich Paschen who discovered it empirically in 1889.