Dan, I think you’re perfectly right that winning a debate and being right are two totally separate things. The hard part about religion is that debate might be the vehicle people use to throw ideas around, but their real reason for their debating is (usually) to assert truth. I have had lots of debates with (supposedly) non-religious people on religion, and although these people try endlessly to stay neutral, they too end up having some sort of opinion. So, other than in formal debate situations (let’s say high school debating club or what have you) I think debating almost necessarily carries with it a gravity that requires the debater to believe what he or she is debating.
So, if, when debating, people really and truly believe what they’re saying, of course it hurts when one feels wrong/unable to one up one’s opponent. I’ve felt this way myself lots of times when talking to people of other religions and/or Christians who I disagree with.
The only way out of this, and this might seem like a cop out, seems to be presuppositionalism. The reasons I don’t think it is a cop out is because, as I’ve mentioned above, I think everybody does this. It’s not rude, archaic, insensitive or judgemental to believe that what you believe is right, iff you have proof/reasons to expand your argument. So, with your starting point, go ahead and make assumptions. However, when you show me/prove to me that your assertion matches reality, give me examples, philosophical proofs, etc.
As a footnote to this, when I do encounter a debate where I can’t win, I try to lose graciously, open-mindedly and faithfully. This means that I (honestly!) tell my opponent they could be right. I’m not God, so even though I truly believe I’m right, it is not my job to be 100% certain about this. The humbleness behind saying (and believing) one could be incorrect is, I think, a form of apologetics in and of itself (I use this method on a regular basis and feel like its a strong witnessing tool). At the same time, I try to prohibit debates like this from ripping apart my personal faith, by investigating the facts people have told me, and praying that God will either give me answers or reveal why the answer to a certain issue can remain inaccessible and the world can still operate around Christian principles.
Presupposing doesn’t always work in a debate, but I’ve looked enough into eternal regresses and skepticism and the like to know that sane people have, and always will start with some kind of assumption or another.