Because "hate speech is driven by the left" is incompatible wiht "hate speech is driven by both sides of the political divide". Those sentences make conflicting claims about the world. The first sentence claims that it is mostly or entirely the left that drives hate speech laws, and the second sentence claims that both the left and the right drive hate speech laws about equally or not so different from equal that it would be worth singling out a particular side.
Because hate speech laws are driven by the left.
You have already admitted that at least one hate speech law was driven by the right.
Therefor is is true that hate speech law is driven by the right.
Given that hate speech law is also driven by the left, it is necessarily true that hate speech law is driven by both the right and the left.
It is a matter of logic.
If you can't agree with that, we have nothing left to discuss.
The statement "Hate speech law is driven by the left and the right" does not imply that both forces are equal. It is illogical to make such a claim. Just like it is illogical to claim "Hate speech law is driven by the left" when not only are the instances of hate speech law driven by the right, but that reality is actually acknowledged.
Think about it. If hate speech laws are stupid or evil, it doesn't matter who or what is driving them. So why the illogical insistence?
But rest assured that neither evidence nor logic will prevent the persistence of posting ideologically driven falsehoods to attack someone's straw men. It is embarrassing to watch. In essence, you are feeding a troll.