Men who claim women are softhearted also tend to harbor dread and resentment toward the female authority figures of their own childhoods while expecting the women in their adult lives to clean up messes without nausea while enforcing social norms without mercy.
There's no room for honest empathy in what misogynist traditionalists really expect from women. Plenty of room for performative shrinking from Others and Think Of The Children rhetorical tricks. Empathy? Nah.