why do electron pairs not take axial positions in the VSEPR structure of ClF3?
Let's take a look at the electronic configuration of $\ce{ClF3}$.  

  

For $\ce{ClF3}$ actually three isomers are possible.  



 

It is highly unfavorable for the lone pairs to be 90° apart which rules one of the three. In order to rationalize the obervation that the isomer with both lone pairs in equatorial positions is the observed form, it is necessary to count the number of 90° bond pair - lone pair interactions. The observed isomer  has four such angles and the isomer with the lone pairs in axial positions has six which is (presumably) less favorable. The molecule might be called T-shaped based on the atomic positions only.