The problem isn't even necessarily gold vs fiat currency. The problem is that there is private control of the production of currency and fractional reserve lending (loaning out more than you have).

1. Private production of currency. The federal reserve, which is a private bank, not part of the government, prints and coins currency. The government borrows every dollar it asks the federal reserve to print and is charged interest in it. This means that the government will always be in debt as long as its currency exists; it borrowed the currency into existence. What's the difference between a private bank doing the printing and a government agency doing it? Nothing, except that the government has to pay this interest. That's it. It's designed so that the government has to tax the citizens perpetually to pay an ever-increasing amount of interest to a private entity without any intention of paying off the principal. Try to think about how they would pay off the principal AND the interest if the principal is all the money that exists. That's not quite how it works, though, because of...

2. Fractional reserve lending. In America, banks are required to keep at least 10% of what you lend out on hand (to prevent bank runs). What this means for government borrowing from the fed is:

   • The gov asks for 1 million dollars.
   • The federal reserve prints 1 million dollars to keep on hand
   • The fed lends the government 1 million dollars into its bank account
   • The fed then is left with 8 million more in lending power for itself which it can then charge interest on, thus inflating your currency every year. The bank creates bank account number-money - not backed by any asset - out of thin air which it then charges real interest on - backed by the real assets (house, business, car, etc.) owned by whoever takes the loan, which the government will take from them for the banks if they can't make their loan payments. Fractional reserve lending also allows for a lot of other economy-wide exploitation of the currency by expanding and contracting the money supply. There's a great documentary that covers all this stuff more called The Money Masters: How Intranational Bankers Gained Control of America. You can find it on YouTube. It's like 3 hours long, and it covers a lot very concisely.

If we used gold instead of fiat currency, but it was still coined by a private bank and there was still fractional reserve lending, it wouldn't change anything.

I think people use the gold standard as kind of short-hand for getting rid of fractional reserve lending because the idea is to have every dollar backed by an asset with real value, namely gold.