I think my girlfriend is incapable of learning anything
What makes you feel this way about her?
She's really cruel to her family, and she doesn't take constructive criticism well.
It doesn't sound like you and she are a good fit or healthy together. Sometimes the best thing is to end a relationship. She doesn't sound nice, and you don't seem to like her at all.
No, I'm going to tell her to stop dumping on her family. They're not my family, but I still care.
It is fine if you offer constructive criticism but i would not continue the relationship, it does not seem to be beneficial to you.