Nobody burned anything. You can head over to his website and watch his videos if you want.

Not giving someone a platform isn't taking their free speech away, any more than me telling religious people attempting to convert me to get off my property is violating their religious rights.

if you had many videos up, and they were all taken down, it is like book burning. they were published, then destroyed.

Alex Jones said trans people murder babies with democrats for their blood...

one can be against censorship and against the message being censored.

in other words : don't assume those that defend people like Alex Jones are defending his opinions.

Many are defending his ability to transmit his message, regardless of the quality of that message, in the interest of preserving that ability for themselves and causes that they support.

Nah, they are using that as a front to push their agenda, because otherwise they'd be super in favor of google and youtube's free speech too, which they are not.

Alex Jones isn't legally prohibited from saying lies about Sandy Hook, and the people up in arms defending those hateful lies and saying we should be careful to preserve hateful lies on private platforms are either idiot patsies or purposefully misleading liars(like Alex Jones himself actually.)

I think you're confusing YouTube's "free speech" with YouTube's ability to censor anything they want. I have no issue with Google uploading YouTube videos or blog posts spreading essentially whatever message the company wants to spread.