When people say things like that, they aren't saying ANYTHING about you, they're making statements about themselves and what kind of person they are. It's like shouting at your kid for being too loud.
NO! Not all parents should be parents. You have the power / choice to figure out who you are. Not her. Do your best mot to believe what she says about you. Talk to a guidance counselor or therapist if this is having an effect on your self-esteem.