Either way is fine, having it the "wrong" direction means smooth rolling of the paper once you get an end to pull, as the acfion pulls the roll off the wall although granted it does mean a little extra faffing to get started.
As for regular, quick easy starting access but a tendancy to bounce off the wall when pulled with any alacrity.
As for the cat argument, had cats my whole life and not once has there ever been an incident of cats pulling down the loo roll, you people evidently arent house training them well enough