My argument in its strongest form

When someone makes a claim publicly, that claim becomes available for public scrutiny. Others are therefore entitled to agree with it, question it, criticize it, or rebut it. This is particularly important when a public claim is false or misleading, because leaving it unchallenged may allow readers to mistake it for an uncontested fact. The original author may choose not to engage with the rebuttal, but that does not give the author authority to prevent others from responding, especially when the response is directed toward the wider audience rather than toward the author personally.

That formulation preserves the force of my argument while avoiding two overstatements:

My strongest principle is therefore not “everyone must answer me.”

It is:

“You may decline to engage with my rebuttal, but you cannot reasonably claim that your public statement is immune from public criticism merely because you do not wish to be challenged.”

And there is an important democratic/intellectual principle underneath it: public discourse is not a private conversation with the original author; it is also communication with everyone who encounters the claim.