Why does parasitic capacitance influence high frequency Dc-Dc switching?
In that scenario, a current would never flow.


Of course current flows through a capacitor each time the pulse rises and falls. For a capacitor Q=CV and differentiating on both sides to obtain current we find that: -

I = C dv/dt because dq/dt = current.

In other words when the voltage edge is sharp (high dV/dt) the current can be very large if not limited by some series resistance or an inductor.

It is for this reason that the current into a capacitor from a sine wave voltage source is shifted by 90 degrees into a cosine wave - it's all down to the maths behind differentiation of voltage (dv/dt).