"[Not] telling your boss you're quitting" is a broad issue spread over many questions, the closest duplicate to mine is probably here. The consensus is that you have no obligation to prewarn employers that you're looking elsewhere and there are unnecessary risks in doing so.
My question is not about what I "should" do (see above) but how to do it. Specifically, how to maintain the above reasonable desire for privacy in the face of my boss' reasonable desire to know my intentions ASAP. This is a simple conflict of interests whereby I'm trying to delay coming clean until I have a new offer and he's trying to catch as much warning of unhappiness graduating to active job search as he can.
Probably this wouldn't even be an issue if I could just do the strategic dishonesty that seems to be so widely justified these days. Morals aside I am simply a very poor liar. My boss by contrast is very experienced at getting things out of people and will have had this specific conversation many times before.
We are having a meeting later wherein I predict I am to be 'cornered'. He will enquire as to my unhappiness. I will give a vague answer. He will ask directly and pointedly whether I'm considering leaving.
What do I say then? Flat out lie? Maybe you can see now the level of response I'm looking for - how do I navigate this social situation, what words do I say?
Let's say I respond "no I've not been considering leaving". He will point to the context of my apparent unhappiness etc., there might be some discussion, but ultimately that'll all be in the service of re-asking the question from a new angle. This will continue for as long as he doubts my answer and can think of new angles from which to pry open my true intentions.
How does one withstand this with professionalism? All the previous answers just say "you shouldn't tell your boss you're going" without recognising the boss' obvious motivation to work against that.
"Just keep giving the same answer" won't cut it without an unprofessional degree of absurdity. Remember he is probably aware of that tactic and actively trying to lever it out of the way. Vagueness will be countered with specificity - lots of 'surrounding' questions again all attacking the central one. How do I answer those questions? I can't just act like a robot with one canned response...