Your parents are mistaken, cats and dogs do get along well together. It will be perfectly safe to drop Fluffy over the fence so she can make friends with the Wilson's Bull Terriers.
And, for that matter, Ah, you say that 3+5 is 8, but what stops it being 18? Consider rejecting the arbitrary axioms of mathematics, and you will see that it could just as easily be 235 or 835 or even five million! Hang on, I'll draw you a diagram.