We'll have to agree to disagree

Both of these things are true simultaneously. Yes, you can protect your privacy at all cost and treat people coldly. You can also cause yourself future difficulties because people don't trust or like you because you've treated them like NPCs and not people. We all have our priorities.

Edit: people don't develop "self awareness" when you treat their polite interest with hostility. They assume things about you because you've given them no other choice.

Think whatever you like. Delivery has a lot to do with it but it still won't make a person feel good and they probably won't tell you that. Nothing about that response would make a person feel you are flattered by their question. It will make them feel you are being cagy and intentionally withholding.

You don't have to own them, no. But, you do have to work with these people so the consequences of burning bridges is still very real.

It's a diversionary tactic which could make a person feel defensive since you are directly choosing not to answer their question.
It could also be interpreted as aggressive or implying the asker has nefarious intent.