I'm going to say to my very insecure cousin that she's arrogant
Why do you need to let her know she's arrogant?
She's so self-centered and she always acts like she's the best.
That is terrible that you want to point that out to her. If she is insecure then she has issues to work through. Why not try and help her so she doesn't come off that way in the future?
Maybe. What happens if I say it anyway
You might really hurt her feelings and cause her to be more withdrawn and insecure. You should try and say nice things to her and not be mean to her. Criticizing her is only going to hurt her more than you think.