Your rights end where mine begin, is the case I'm making.
By forcing me to offer you a platform you're violating my rights to free speech. A right to speak must also follow a right not to speak in the way freedom of religion must also necessarily involve a freedom from religion. You can't make me, a private entity, tell your story in your words. I certainly don't expect Breitbart to publish my feelings on how America doesn't have a "left" using my words. Should I be able to force you to publish my essay on your blog?
I can't actually think of a time when "free speech" as you describe it ever existed. There's never been a country where media was required by law to publish whatever was given them. Certainly not in feudal days, not in the industrial revolution, and not today.