The main source of confusion here is that "your bank account" is actually two different entities whose numeric value happens to be the same:
1) On your books, it is an asset account.
2) On the bank's books, it is a liability account.
When a bank says "your account was debited", they are talking about entity #2. That is, "the account on our books associated with 'you'".
But when you yourself think of the account, you think of thing #1.
Let's say you deposit some cash into your account at the bank. That means you are lending the bank the money (extending it credit). The bank records this as two transaction entries:
* A debit (receiving money) transaction which places more money into their general "money we have" pool: you gave them money.
* A credit (owing more money) transaction: they now owe you more money. This increases the amount of what the bank thinks of as "your account".
The statement they send you at the end of the month only shows the second transaction, because that's the one relevant to "your account" in the sense of #2 above.
If you were keeping books on your side, you would likewise record this as two transaction entries:
* A debit (receiving money) transaction for your bank account (now in the sense of #1 above).
* A credit (having less money in an asset account) transaction for your wallet.
So the upshot is that in the two entities that "your bank account" corresponds to, a debit for #1 is a credit for #2 and vice versa. And when the bank sends you a statement, it describes #2, not #1. Since most people don't interact with the terms "debit" and "credit" normally, this is the only exposure they have to those terms, so they learn them backward....