It's correct that "debit" and "credit" don't have to do with "owing/being owed" money. But they do have to do with "OWNing/being owed". This apparently subtle difference provides powerful insight.

If you look at equity as money owed to shareholders, then the left side of the balance sheet is money owned, and the right side of the balance sheet is money owed.

  Money OWNEd = Money OWEd

  Assets      = Liabilities + Equity

A debit either increases money OWNed on the left side of the balance sheet, or decreases money OWEd on the right side.