According to the Guardian's Andrew Sparrow, a spokesman for the Judicial Office has explained:
'This was a case in which the Home Office conceded that they had mistakenly failed to apply their own policy - applying at that time to that appellant - for dealing with unmarried partners of people settled in the UK. That was the basis for the decision to uphold the original tribunaldecision - the cat had nothing to do with the decision.'
"why did the Home Office lose this reconsideration? Because it had failed to follow its own guidance...had the policy been properly applied, the immigration judge would have had to allow the appeal anyway, cat or no cat."
So, the decision not to allow this man to be deported had nothing to do with him owning a cat. In fact, it seems Theresa May was regurgitating myths peddled by the press a couple of years ago and debunked at the time.
Chalk one up for Ken Clarke.