Only provable lies should be censored. Provably factual claims should not be censored. unprovable or disprovable subjective beliefs and opinions should not be censored - to the extent that they are being presented as belief and opinion and not as fact.
For example, I should not be able to advertise a homeopathic product as being an effective, curative treatment for cancer and giving all manner of provably false medical claims to back my advertisement. That should be illegal.
But I should be able to say that I believe that taking this product will cure cancer without presenting any false factoids to support my belief.
Here's why free speech, in the context of permitting the dissemination of offensive beliefs and opinions is good: The offensive beliefs and opinions get to be scrutinized and criticized with facts and logic, thus exposing them as being foolish or false. In such an environment, it is near impossible for tyrants to rise and mislead the masses and blinding the collective mind and conscience by silencing dissenters.
On the other hand, censoring information just because it's offensive - that's equivalent to banning a medical treatment just because it has unpleasant side effects, regardless of how effective the treatment is and regardless of how harmless the side effects are. What happens when a truthful and beneficial statement is banned because it is offensive because the offended is indoctrinated into a twisted and harmful mindset? The beneficial information that can free the indoctrinated is suppressed and the twisted, harmful mindset persists to the further detriment of society!
So permitting free speech creates an egalitarian, self-correcting environment where survival of the fittest ideas - fittest to reality - pertains, with ideas being vetted, challenged and rejected or accepted by the collective judgement of a plurality of diverse minds.
Censorship creates dictatorial environment where survival of the ideas of those with power, pertains. The validity of an idea is easily relegated to lesser importance than the preferences of those in power.