It doesn't imply that at all.

History shows us it does. The people who used to run the ACLU were very well aware of that.

> What's a more fundamental right, life, or speech?

Could you help me understand how "history shows us" that this question implies that the loss of free speech can't be a threat to life?

Sure. Nobody dared speak up against the Holocaust. (Those that did were sent to a labor camp or had their heads sliced off.) Lack of free speech meant the Nazis could (and did) kill anyone for any reason with complete impunity. There was no right to life under Hitler.

The first thing dictators do is remove free speech. This is what enables removing all the other rights at the dictator's whim, because then nobody can speak out against it. Nobody can even inform others about it. This is why totalitarian regimes so aggressively suppress free speech.

The Soviet Union collapsed soon after Gorbachev stopped repressing free speech (glasnost and peristroika). This is not a coincidence.

Still not sure how the question implied that the loss of the right to free speech can't threaten life.