Specifically, we do not know whether the credit card ends up on your server (possibly stored poorly), and just knowing you use Stripe (which allows for that not to happen) doesn't guarantee that your server has the requisite security required to not have been modified to send the things we enter to a third party.
(That said, I will say that I am not actually the kind of person who fears using my credit card online, so I may be simulating this argument train incorrectly; these thoughts go through my head, but my reasons for often using PayPal when provided the option have more to do with liking the kinds of reporting I can easily do using their APIs.)