Of course it does, somebody whether it is a nation or a website or a piece of paper has to host your speech. Otherwise it will just be thoughts inside your brain.
A newspaper doesn't have to publish your op-ed. YouTube doesn't have to host your video. You can make a website for free to get your point across without going through Youtube, so they're not silencing you either. Not in a free speech sense.
You're just not entitled to forcing others to express your speech for you.