Is current direction always opposing when signals are reflected on a transmission line
My understanding is that this negative voltage arises from the need to supply "additional" current into the short (2*I behind the reflected voltage wavefront). But then, isn't the current moving towards the short 


Yes, you are correct.

If the termination is purely resistive, with value less than the line's characteristic impedance, then the current at the point of termination will be in the same direction for the forward and reflected waves.

If the termination is purely resistive, with value greater than the line's characteristic impedance, then the current at the point of termination will be in the opposite directions for the forward and reflected waves.

But if you consider points on the line at some distance from the termination you could see the forward wave and reflected wave currents either constructively or destructively interfering in either case.


  In the snippet shown below, you can see where the reflected current is described as having the opposite direction to the incident current.


The snippet gives the eqautions

$$I_F = \frac{V_F}{Z_0}$$
and
$$I_R = \frac{-V_R}{Z_0}$$

Remember that in the case of a reflection from a lower resistance load (or short), \$V_R\$ will have opposite sign from \$V_F\$ (at the point of reflection), so there is no contradiction.