Why can I not get a unsecured credit card?

It's rather difficult to give a straight answer as you have provided too little information. First and foremost, it depends on your credit score. Probably, you have applied for a credit card that doesn't suit your credit, and that was the reason of your failure. Obviously, you've got average or limited credit history if you have been rejected to get an unsecured card. But in fact there is a number of unsecured credit cards specially designed for those with average or limited credit, like Standard Platinum Card by Capital One. This card offers really great terms for those who continue building credit history: 0% Intro APR on purchases, no annual fee, and more. You can also review Capital One Platinum Card that comes with a low ongoing APR and the interest-free period. In case you've got a spoiled credit history, you may consider Orchard Bank Classic MasterCard. This card is issued for customers with bad/no credit so the chances are you'll be approved for the card. Anyway, before applying for a card, you'd better check your credit score and choose the card in accordance with your credit rating.