Insecurity card is an idiomatic phrase that refers to the act of bringing the issue of insecurity into a debate or argument. Women are notorious for accusing their husbands/boyfriends of being insecure for almost anything and everything (even if it's not true).
Bob: Hey Mike, I saw you leave your house last night. What happened?
Mike: I got into a fight with that biatch again. She pulled out the insecurity card like always.