One of the common threads I've noticed across many people when trying to explain why defending freedom of speech, and the free and open exchange of ideas in general, is that they're not just defending some "right-wing" person's rights, they're actually defending their own rights. Because the same tactics and rationales that are being used to suppress and silence the "right-wing" (which is comically everyone to the right of Bernie Sanders these days) will eventually be turned around and used to silence and suppress them.
But so many people simple can't wrap their head around it.
The notion is perfectly illustrated by Sir Thomas More in A Man for All Seasons:
William Roper: “So, now you give the Devil the benefit of law!”
Sir Thomas More: “Yes! What would you do? Cut a great road through the law to get after the Devil?”
William Roper: “Yes, I'd cut down every law in England to do that!”
Sir Thomas More: “Oh? And when the last law was down, and the Devil turned 'round on you, where would you hide, Roper, the laws all being flat? This country is planted thick with laws, from coast to coast, Man's laws, not God's! And if you cut them down, and you're just the man to do it, do you really think you could stand upright in the winds that would blow then? Yes, I'd give the Devil benefit of law, for my own safety's sake!”
By protecting the rights of everyone, even people you disagree with, you are ultimately protecting your own rights. Anything else is short-sighted and dangerous.