Hate speech argument fallacy?

I can't quite put my finger on it but I can't help but think this argumentative statement is fallacious:

Hate speech cannot be made illegal in a consistent way: outlawing hate speech would be an expression of hatred towards hate speech, which, by the proposal, is to be made illegal.

Even if we accept the preposterous inference that a law is "hatred toward that being made illegal," it is not all "expressions of hatred" that is being outlawed; it is only one expression: speech (verbal and written). There is a clear strawman fallacy involved and perhaps equivocation .

Side note: I agree with the claim that "hate speech cannot be made illegal in a consistent way" but for the reason that what counts as "hate speech" varies greatly depending on who's making the rules. As an outspoken atheist, I would not want my arguments against the God of the Bible to seen as "hate speech" (against God).

Maybe I am missing something, but I see this as complete nonsense. If we take the implied premise that one must hate that whichever is being made illegal, which means you must hate hate speech, then I don't see how the conclusion that hate speech cannot be made illegal makes any sense. I think this is a non sequitur 

The paradox being used in an attempt to support the initial claim is a variation of Popper’s Paradox of Intolerance. It is the idea that “in order to maintain a tolerant society, the society must be intolerant of intolerance.” Essentially, if a so-called tolerant society permits the existence of intolerant philosophies, it is no longer tolerant. 

The main problem here getting from the claim to the paradox. First, one would have to demonstrate that legislation is truly an “expression of hate.”

Second, (and more fatal to the scenario argument here) is that hate speech is defined as “expressions that advocate, incite, promote or justify hatred, violence and discrimination against a person or group of persons for a variety of reasons.” This latter part is the slippery bit as the initial scenario tries to point the target of hate speech from people to speech itself—which by common usage, would disqualify itself as “hate speech.”

Dr Bo made a good suggestion with equivocation. There's a clear difference between hating something and hate (hostility and prejudice towards a person based on a protected characteristic, like race). 

A law against 'hate speech' would address the second, not the first.

This person is either deliberately making a misleading argument, or, charitably - they do not understand what a hate speech law entails.

Always start with definitions of the main tenets of the argument, which in this case is the word "hate." The participants must first cross the hurdle of agreeing on a definition. 

However, I think you are correct that "Hate speech cannot be made illegal in a consistent way" because of so many variables. For example, I am an atheist, and a common statement made to me is: "You hate God." To be an atheist means one who does not believe in any of the 5,000 known gods humans worshipped over the years. It is a non-belief, not an affirmative statement such as "there is no god." Logically, one must ask, how can one "hate" something one does not believe exists? Which is nothing more than saying hate speech is anything the speaker disagrees with. Sort of like the buzzword "misinformation."