Each seller using eBay is like a shop at the mall.
We share selling space but operate independently.
Very few sellers have merchant credit card accounts that allow them to take cards directly.
Instead we use Paypal, which allows buyers to send us money* without the seller ever seeing the buyer's financial information.
When you sign up for Paypal, which if free to the buyer, your financial information is strictly confidential. You can pay with confidence. There is a short delay in opening the account while PP puts a few cents in your bank account and then removes it when you confirm they have the right account.
If you are in that situation, let the seller know. It will give her confidence too.
*from a credit card is easiest, fastest, and most secure, but you can attach your bank account or even hold a balance in the PP account.