Exercises such as 'pushing hands' must be seen in the wider context of the tai 
chi. 
They are not an end in themselves. 
Pushing hands is a learning tool for teaching skills that must eventually be utilised in 
self defence.
However, pushing hands is not an a combat skill in its own right.
No sane person would believe that pushing hands enabled them to use
tai chi in a real-life combat situation.
The exercise is about contact and sensitivity, feeling and stickiness, learning 
to sense using your nervous system rather than your thoughts.