Diary of the future (women are strong, men can run)
One Piece (Male Violence at Critical Moment)
Accelerate the world (the man is a "fat pig", but the critical moment is very powerful)
Sword world (both men and women can run)
Something falling from the sky (the woman is fleshy and the man sometimes runs away)
Mentor (in a strange way)
Inuyasha (very classic)
Silver soul (even a wooden knife man who loves sweets will run away)