Do I (a man) play different with female players? Yes. I accept draw even if I leads. Why? I don't know.
You have a sense of chivalry. That is very sweet but it has no place in chess. Giving an undeserved draw isn't good for you and isn't good for your opponent. It's an affront to another lady, Caïssa.
Do I (a man) play different with female players? Yes. I accept draw even if I leads. Why? I don't know.