The phrase implies the person’s behavior is socially unacceptable, making others uncomfortable or embarrassed to be with them. Every time we go out, she speaks so loudly. I can't take her anywhere!
Pro Tip 2/3
Light Humor
Sometimes used in a joking manner among friends to playfully criticize someone's minor social blunders. You spilled your drink again? I can't take you anywhere!
Pro Tip 3/3
Not Literal
It's usually an exaggeration and doesn't mean the person will literally never be taken to social events. You keep mispronouncing the waiter's name - I can't take you anywhere!