The problem with using credit/debit directly is that it requires the customer to trust you with their credit card number.

The nice thing about Paypal is I click the button and a window pops up that Firefox recognizes as coming from Paypal to autofill my login info, then Paypal confirms the payment info and gives the website just the payment info. With a credit card, even if you have a different payment processor with an icon next to it that says "secure", there's not actually any way for me to be sure at a glance that that isn't Stripe_Secure_Checkout_Confirmation.SVG and that you aren't just harvesting my credit card info, other than other contextual information on your website and your company's reputation as an actual company that does actual business in the real world.