"I can't take you anywhere!" is something that:
- a parent might say to a child, or
- a girlfriend might jokingly say to her boyfriend (or vice versa), or
- a wife might jokingly say to her husband (or vice versa), or
- a good friend might say to another good friend.
In the context of a parent saying this to a child, imagine a world where "children are to be seen and not heard." Or less severely, that a parent should only bring a child to public places when the child knows how to be reasonably well-behaved, not scream, not make messes, not make offensive remarks, and generally not cause problems for other people. If a mother concludes that her child has not learned to avoid causing these issues, then the mother might conclude that she cannot politely take her child "anywhere" that these issues are problems. "I can't take you anywhere!" is a common way for an exasperated parent to point out (to the child) this consequence of the child's behavior.
In the other contexts, the humor is that the words are said almost the same way that a parent might say them to a child, but that the girlfriend/wife/friend really does enjoy being out in public with their boyfriend/husband/good friend -- except for this one "problem".