1. Borrowing money does not create inflation.
2. Fractional reserve banking is a great way to make money capital available to people who want to invest.
3. Social Security, Medicare, and employer "health insurance" all deprive banks of savings, which deprives the people of earning interest from successful businesses.
4. A fraction is a rational number, which are part of the Real numbers.
5. If my bank tells the Federal Reserve "I have $100M in savings" and the Fed tells then, "okay, now you can loan out $200M!", that is not a fraction. That is an imaginary number.
6. Imaginary reserve banking causes inflation.
7. Only government has the power to legitimize imaginary reserve banking.
8. Who are the shareholders of the Federal Reserve? "Twelve regional Federal Reserve Banks ... Nationally chartered commercial banks are required to hold stock in, and can elect some board members of, the Federal Reserve Bank of their region." But the Federal Reserve Board of Governors can overrule the regional banks. Two are presidential appointees, the rest are appointed by the President with Senate approval.

It's not a private bank, it's a government bank with private bank participation.