No individual owes me that, but this goes far beyond that. You have to keep in mind that any oppinion shared on line represents more than the person expressing it. And it may change the minds of others reading it. If anyone who works on controversial subject X gets a label of unethical that's not just "not owing them a reasonable discussion", you're impacting their life. Potentially ruining it.
Given your stance here, you're perfectly ok with the baker refusing to sell a wedding cake to a gay couple, right? Because the law was effectively the sea lion in your comic.
How so? Stating your thoughts with conviction ends any hope of a reasonable discussion? Maybe if you're afraid of confrontation. For me it's an invitation to debate.
You find labelling people is in invitation to a debate? So if you find yourself in a position where you desperately need a job but upper management says "I think people of race X are <racial slur>" you would take that as an invitiation to a debate? Saying a person is unethical is labelling them. That's what I object to, not debate or confrontation.
> I haven't shut down any argument by saying this
You're being naive if you think that saying this doesn't end any hope of a reasonable discussion.