Dude.
If I borrow $100 from you, what happens? I have $100. I’m rich! I have an asset of $100. But uh oh, I have to pay you back. I owe you $100. That means I have a liability of $100. I have $100 but I owe $100, which means my net assets plus liabilities is $0.
Fractional reserve banking has nothing to do with it. You could have loaned me your last $100 and now you’re broke. You could have a million dollars under your mattress. It doesn’t matter how much money you have. I borrowed $100 so I have $100, but I owe $100 and $100 -$100 = $0.
If I’m a bank then sometimes we say that you deposited $100 with me and now you have a $100 account at my bank.
But that deposit is a loan. You loaned me $100, but I have to pay you back. The only good news for me is that for a while, until I pay you back, I have $100 that I can do whatever I want with. Like, you know, loan it to someone else, or spend it on hookers and cocaine, or squander it.
The only thing “fractional reserve banking” means is that if I have $100 in assets, the Feds will require me to keep $10 under the mattress for emergencies, I can’t lend out the whole $100, or $200. I can only lend out $90. I can’t lend out everything, I can’t lend out more than I have, I have to keep some on hand. And if I go below that amount, I have to get it from somewhere. The Feds don’t just give me the money.
Borrowing money creates an asset and a liability at the same time because that’s what borrowing money means. If it just created an asset it wouldn’t be borrowing, it would be getting. If it was just an asset then I wouldn’t have to pay it back, and I’d have an asset of $100 and $0 liability, so I’d be +$100. If it was just a liability then I would owe the money but I wouldn’t have the money, so I’d have $0 with a $100 liability so I’d be -$100. If I borrow the money and have it, then I’m $100 -$100 =$0.
Contrariwise, if you lend me $100, then you have a liability of $100, because you no longer have the money you lent me. It’s gone! You gave it to me. But you have an asset of $100, because I have to pay you back. And so -$100 + $100 = $0. You have the same net value as before.
If you’re confused that I can borrow money and lend money at the same time and so have assets from the money I borrowed and liabilities from the money I borrowed, and then I lend money so I have assets from the money I lent and liabilities from the money I no longer have, then welcome to the club. Math is hard!