Nonsense.  It has nothing to do with "hate".  Nor is it some cartoonish, simplistic dichotomy of "dogs vs. cats" or "cats vs. birds."

Naturally-occurring systems of animals and plants have evolved together over millennia, struggling to eat and not-be-eaten, until they achieve mutually-sustainable balances of numbers were prey species don't exhaust their food supply and then starve, and predators don't eliminate their prey and then starve.

Invasive domesticated animals like cats and dogs have no place in this system.  They never existed in nature.  They're genetically-modified (by way of generations of selective breeding and ruthless culling), and only occur in the wild because people PUT them there.  The more invasive species introduced into a biological system, the more unstable it becomes, the longer it takes to stabilize, and the more extinctions of native biota result.

But cats are particularly destructive because they kill by reflex, not for hunger.  We bred them that way.