If you give out a business card to someone you think can help you, you are then doomed to waiting around for that person to contact you. If you TAKE his or her business card, then you control the relationship and you reach out when you want with the message you want.
Having business cards is great if you are out of work or if you are a student, and giving them away is also fine. Just don’t give them away with the expectation that anyone is going to use it for follow up. For that, TAKE a business card.