There’s a lot of history that we are not privy to, so it is hard to give specific suggestions for your friend. Since you say the girl is saying this when she’s not getting her way, I’m interpreting it as her attempt to be manipulative and guilt the mother into giving in.
When my son tried to manipulate me emotionally, I’d say, “Mommy don’t play dat” (a reference to the In Living Color clown that was popular at the time, who said, “Homey don’t play dat”) to indicate that I wasn’t going to be manipulated or negotiated with. Then I would address the misbehavior that he was trying to weasel his way out of, which is best dealt with in the moment.
When things were more calm, I always explained that regardless of the circumstances of his birth (I wanted kids, but I wanted them after grad school – not during), I was glad to have him. I also was quick with praise and affection and since I was a single mom, we spent a lot of time together. Admittedly, when he was younger, I was more invested in my social and love-life than I should have been, and once I realized that, I made amends to be mentally present, as much as physically present.
I also frequently pointed out that I loved him enough to put in the effort of teaching him how to be a responsible, independent person; in comparison to his friends’ parents who were easily manipulated, worried about being ‘cool’, and who did everything for the kids. I used the situations his friends went through as examples. By the time he was 16, he was able to recognize how needy those kids were, and he was thanking me for having been tough and letting him learn to think through his decisions and consider potential consequences.
“Mommy is not my name, it’s my job title” was another phrase he heard many times. This helped objectify the act of giving him responsibilities and disciplining when he misbehaved. Now he’s in his early 20s, and now we are friends. He has been working his way up at his job for close to 4 years, pays all his bills, and goes to college part time. He’s not perfect, but he’s been through a lot, and I am proud of him.