Because we don’t have the brute physical and social power that men have.
Dad, like all men—even if he is as gentle as a fawn—implicitly has the power to take your life, beat you up, and take away your rights. Even if he would never hurt a fly, he has the implicit ability to punch people’s lights out and mow them down with his brute strength. He also has the power to marginalize those with less brute power than he has. This is patriarchy. He doesn’t have to want it, ask for it, like it, or even use it once. He just has it.
Mom, while yes, she COULD kill, does not have the archetypical social backing to do so. Even if she is as tough and warrior-like as Queen Boudicea, she does not have the same kind of sway. She does not have that brute physical and social power. Accordingly, she has a lot fewer options for surviving and getting what she wants and needs in the world, and for her children.
This relates, in a way, to the saying “men fear women will laugh at them. Women fear men will kill them.”
In terms of personality problems, men tend to go antisocial (stealing cars, dealing drugs, raping, getting in fights) while women tend to go borderline (threatening suicide, self-harm, self-destructive promiscuous behavior, rages followed up with frantic efforts to make you stay and promise you love her, changing identity to conform to what you want).
Dad wields a different kind of authority within society even if he personally is a groovy hippie pacifist who would never raise a hand at you. He has the right, according to society, to control you with some force, even if he doesn’t do it. Mom finds herself in a position more akin to that of an overgrown child. She has no right to do anything, but she can be, as the movie says “the neck that turns the head.” She can manipulate, from backstage.
Feminists who don’t want to look at this head-on are wasting their time because if you can’t deal with this basic issue, your feminism will be nothing more than male liberalism with a girl power armband on.