Why is the capacitance of a short infinite?
The voltage across a short circuit is zero, regardless of current.

There are three components this could be modelled as, which also have zero AC voltage across them regardless of AC current, they are

a) A resistor with zero resistance
b) A capacitor with infinite capacitance
c) An inductor with zero inductance

However, these components aren't equivalent. 

At DC, a capacitor can have a steady voltage across it, storing energy, and able to deliver that energy into a load.

At DC, an inductor can have a steady current through it, storing energy, and able to deliver that energy into a load.

Obviously therefore, a short circuit only is a zero ohm resistance, as it doesn't store energy. 

However, if you are doing an AC analysis, and have a large value decoupling capacitor, it's often convenient to model it as 'an AC short circuit', as its series impedance will be very small with respect to the surrounding components.