"Debate me, you coward!"
Are you skilled at debate, then?
"I'm the best!"
So you would agree that there is such a thing as debate skill?
"Of course!"
Ergo, the outcome of a debate is contingent upon at least one factor other than the veracity of the position being defended?

"Uh... yes?"
Then a debate between us would only demonstrate that you are 'the best' at debating (a claim I am happy to concede), and would, in no way, disprove my ideas. You could, presumably, argue that the world is flat and still debate circles around me.

"No, a debate shows who's right!"
So the party with the correct view always wins debates?
"Yes."
Then you don't need me. Literally anyone else could argue my positions with equal effectiveness. Presumably, you could play devil's advocate and argue both sides against yourself.

"You're just scared to debate me in public!"
Oh, I'm positively terrified. You're so much better at debating than I am, after all.