You can never convince a woman of a truth that shows her in a bad light. She feels no guilt so your truth doesn't fit her in her mind.
This is why women can totally ignore a man's rational and logical conclusions, utterly dismissing them of any shred of worth, without a flicker of cognitive dissonance. It's not even a speed-bump to the spinning hamster.
That said, it's a good thing to be able to debate a woman. Doing it properly requires two things:
1/ The ability to know exactly when she's trying to reframe the debate (aka change the subject or make a personal attack on you)
2/ The guts to point out that she's trying to dodge - and agree'n'amplify is a good tactic to defuse any personal attack on you
Just remember to keep drawing the "debate" back to the subject, or (eventually) laugh in her face and say something along the lines of: "Since you're too chickenshit to actually answer the question/finish the debate, I win!"
Declare it as a fait-accompli and go do something else more interesting.
Then just laugh at her and practice your amused mastery when she gets shitty with you for calling her out on her shit. Note that defensive vagina-tingles may ensue, in which case you could get some poontang out of this.