I don't have the option to have no credit card, and I can't continue with my account setup. And this is through an iPhone4. What would be the cause of that?

When I got this phone I had to input an Apple ID, which I did, but it never had the option to have no credit card. I assumed that I HAD to have a credit card so, my mom allowed me to use hers. Eventually, her card ran out of money and so, the store would not allow me to download anything. It would send a message saying "There was a problem with a previous purchase. Please, tap continue to view billing information." Afterwards, I got tired of not being able to download anything so I thought that if I just make a new account, it might allow me to have the "no credit card" option, but when I started making it, it didn't even have that option.