The Paradox of Tolerance was an argument put forth by Karl Popper which describes the circumstances under which it would be justified for a society committed to the principle of tolerance to forcibly suppress the expression of certain ideas. Karl Popper believed that a tolerant society would be acting in the interest of tolerance by silencing those with "intolerant" views when the expression of those views would threaten the tolerance of the society. According to Popper, if one is in favor of tolerance, then one should seek the maximize it, and this sometimes requires fighting intolerance with intolerance. On the other hand, if one is not in favor of tolerance, then one has no reason to complain if the intolerant are suppressed. Either way, according to him, the principle of unlimited free speech is indefensible.
The main flaw with the argument, or at least with its modern interpretation, is that "tolerance" is being used in two different senses. A society incorporating free speech as an absolute principle need not be a society committed to tolerance in any wider sense. That is to say, an ardent defender of free speech is only obliged, according to the argument, to suppress views that directly threaten free speech but not any other kind of "intolerance". They can want society to be tolerant of more than just people's speech, but they need only maximize free speech itself and not any other kind of tolerance in order to be considered a "true believer in free speech". Those who insist that society suppress intolerant views which don't call free speech into question cannot rely on the argument that "If free speech is good, then this person, whose views are at odds with free speech, must be silenced in the name of free speech". Instead, they have to rely on the a priori assumption that a view is bad if it is deemed by society as "intolerant". But this is no more justified than society trying to silence all views the majority considers "wrong", whether or not "intolerance" is the reason they are deemed wrong.
At most, the Paradox of Tolerance requires that society prevent people from speaking out against free speech, and arguably, this would entail suppressing those who interpret the Paradox of Tolerance to mean that silencing all "intolerant" views is consistent with the principle of free speech.