Why do liberals love censorship?

Because it works.  As we are seeing once again.  The big break away for the Chick fil A controversy was that it was elected government officials using the power of their government offices to banish a company based on the free speech of its top official.  Sort of like those old time puritans whipping a Quaker out of town on a cart, these liberals (and boy do I use that term loosely) are invoking the same inquisitorial Orwellian censorship.  Why? Because they can.  Because America, like so much of the world, has tried freedom and liberty and found them wanting.  Now, as liberalism has firm control over the venues of information in our culture, it's only a matter of time before rejecting leftist dogmas will get you all the tolerance as supporting the Soviet Communists did back in the 1950s.