Bitcoin created decentralized trust. Understanding the implications of this are critical in understanding bitcoin.
As OP described wonderfully above, our current system relies on a bank to act as a trusted third-party when two parties are transacting. For example, when I swipe a debit card at a store, the bank tells the store that I have enough funds to pay for my items. The store trusts the bank response, thus trusting me to walk out of the store with merchandise and that they will be paid.
Bitcoin shows that trust doesn't need a centralized third-party (i.e. banks) to establish trust. You can have a decentralized network of trust instead. People can easliy, safely, and securely transact on this network of decentralized trust. This is ground breaking. It completely disrupts a major value proposition for banks.
My idea will help the beginner understand to bitcoin.