Why is asset = liability + equity? Shouldn’t it be asset = equity - liability because assets put money in your pocket. Liability does not?

Asset = liability + equity
Net assets = asset - liability = equity.
Still the same thing.

Your 2nd statement is not looking at things in the right way.

Lets use a simple example. Bf and gf have saved 50k and plan to get married and buy a HDB flat worth 300k.

But 50k not enough. How? The couple borrow 250k from bank on a loan called mortgage.

So asset = hdb of 300k = paid with 250k of mortgage and 50k savings or couple's equity.

Its balanced. Net asset = 300k of hdb - 250k of debt = what couple has in savings.

Liability and equity are based around the concept of ownership. You have the hdb flat, but you do not "own it fully" because if you dont pay off the mortgage, the bank will seize it. Your ownership is the 50k you paid upfront for.

Does this make it simpler?

Asset = liability + equity
I am merely using a very simple way to explain.
From the perspective of the company,
liabilities are money the company owed to creditors whereas equities are money owed to shareholders. Assets are what the company bought using the money from creditors and shareholders. That is why assets = liabilities + equities. Hope it helps in your understanding.