That's (somewhat) true for accounts that represent stocks (assets, liabilities, not really for equity though), it's not true for accounts that represent flows (income, expenses). Income is recorded as a credit entry in an income account, eg (the corresponding debit entry would typically be on something like a current account or claims on customers).

Consider the positioning of income and expense accounts within the accounting equation. Essentially, they are components of equity. View equity as the company's obligation to its shareholders. A credit entry signifies an increase in what the company owes, whether to creditors or shareholders, while a debit entry reflects an increase in the company's assets.

Isn't that exactly backwards to what most people think of credits and debits? If you credit me something, I now have something. I don't owe anything.

I can kinda squint and see "Oh, you want the universe to balance, so if I have something it is some kind of karmic debt". But it still feels like exactly the opposite of what I grew up thinking of these terms to mean.

It's the opposite because when a counterparty (like a bank or a store) says they're 'crediting your account', they're talking about the impact from their perspective, not your perspective.