> The common English use of 'credit' and 'debit' is correct,
Yes, by definition.
> The mistake is that we talk about them as "our" accounts.
No. The mistake is the failure to recognize that every account is actually two different accounts, one for each party to a transaction. A bank account looks different to the bank than it does to a depositor or to a borrower. To a depositor, a positive balance is an asset -- quite literally "money in the bank". To the bank, a positive balance in a deposit account is a liability, a loan that it has taken from the depositor on which it must pay interest (at least sometimes) and which it must eventually pay back. To a borrower, a positive balance on a loan is a liability, to the bank it's an asset. Every financial asset is a liability to some counterparty. Even cash is a liability to society at large. So whether something is an asset or a liability depends entirely on your point of view, and so if both parties are going to use the same number to represent an account balance, it is an arbitrary choice what the sign represents. A positive number is always going to be an asset to one party and a liability to the other. Which is which is totally arbitrary, except that there are some deeply entrenched conventions: a positive balance on a deposit account at a bank represents an asset to the depositor, a liability to the bank. A positive balance on a loan represents an asset to the lender, a liability to the borrower. A positive balance on an invoice represents an asset to the seller and a liability to the buyer. But there is no inherent reason why it has to be that way, it's just tradition.
Likewise, whether "credit" means "increase" or "decrease" is also simply a matter of convention. A "credit" to a deposit account means the balance goes up. A "credit" to a loan account (i.e. a loan payment) means the balance goes down. The thing that unifies these things is that a "credit" is either an increase in an asset or a decrease in a liability since both assets and liabilities are recorded by convention as positive numbers. So in isolation (i.e. without a balancing double-entry transaction), a (positive) credit increases your net worth and a (positive) debit decreases it.
Yes, by definition.
> The mistake is that we talk about them as "our" accounts.
No. The mistake is the failure to recognize that every account is actually two different accounts, one for each party to a transaction. A bank account looks different to the bank than it does to a depositor or to a borrower. To a depositor, a positive balance is an asset -- quite literally "money in the bank". To the bank, a positive balance in a deposit account is a liability, a loan that it has taken from the depositor on which it must pay interest (at least sometimes) and which it must eventually pay back. To a borrower, a positive balance on a loan is a liability, to the bank it's an asset. Every financial asset is a liability to some counterparty. Even cash is a liability to society at large. So whether something is an asset or a liability depends entirely on your point of view, and so if both parties are going to use the same number to represent an account balance, it is an arbitrary choice what the sign represents. A positive number is always going to be an asset to one party and a liability to the other. Which is which is totally arbitrary, except that there are some deeply entrenched conventions: a positive balance on a deposit account at a bank represents an asset to the depositor, a liability to the bank. A positive balance on a loan represents an asset to the lender, a liability to the borrower. A positive balance on an invoice represents an asset to the seller and a liability to the buyer. But there is no inherent reason why it has to be that way, it's just tradition.
Likewise, whether "credit" means "increase" or "decrease" is also simply a matter of convention. A "credit" to a deposit account means the balance goes up. A "credit" to a loan account (i.e. a loan payment) means the balance goes down. The thing that unifies these things is that a "credit" is either an increase in an asset or a decrease in a liability since both assets and liabilities are recorded by convention as positive numbers. So in isolation (i.e. without a balancing double-entry transaction), a (positive) credit increases your net worth and a (positive) debit decreases it.