In effect, we’re paying for two things - the website and associated features, and financial transaction processing.
Setting up payment processing, and managing it, can be a difficult task, if you can even get a payment processor to give you a personal account,. That alone is worth the fees, at least for me. And remember, part of the fees Patreon charges are to cover the fees that the banks, credit card companies, and other payment processors charge. You can’t escape those unless you deal only in cash.
As for the site, while I’m a critic of Patreon at times, I know that running a site like this takes a lot of work and requires significant resources. I could, in theory, run my own site, and manage all the software, and so on, but that would cost me far more than the fees Patreon charges (and most people aren’t PHP/web coders who are also Unix system engineers, which I happen to be).
That said, I see no reason why I wouldn’t take payment for my work in other forms and in other places. I sell my writing through a virtual bookstore in addition to the occasional ‘private sale’ that doesn’t use either of them. I’ve never been paid in cash, but I’d accept it if it were the only way someone could/would support me.
As for the safety and security of your payment (and other) information, there are serious rules and regulations imposed by the payment processors. See: https://www.pcisecuritystandards.org/ . I’ve implemented those during my IT career and they are very thorough. Any site that consistently violated those would lose their ability to take payments.
So, bottom line - take payments however you want, but explain to your friend that the site and services cost money to provide, and that it’s not at all likely you could do it yourself, and if you happen to be someone who can, it’ll cost far more than Pateon charges.