When a bank gives you a loan, it isn’t fully backed by their deposits. Thanks to fractional-reserve banking most of the money is created when the loan is issued.

My question is: why can’t private citizens create their own bank and issue loans to themselves?

You’d deposit 100k€ in your own bank and, given a 10% reserve/capital requirement, you’d be able to issue yourself loans for up to 1m€. Your bank sells the loan to some fool (central banks will gladly buy it nowadays, yey!) and you soon end up with 1m€ of cash in your personal bank account.

I guess the state considers current bank owners more equal than others citizens in the end.