Why is my Apple Pay asking for social security number?

I suspect you are talking about the Apple Card or Apple Cash. It is not Apple asking for this information, it is the bank for the account you have opened, and Apple is not a bank. Identify verification is required for any bank account, and for Apple Cash, it usually kicks in once you reach a certain threshold in transaction amounts.

Verify your identity for Apple Card or Apple Cash - Apple Support

It is also seen in the Terms & Conditions for Apple Cash:

To help the government fight the funding of terrorism and money laundering activities, federal law requires all financial institutions to obtain, verify, and record information that identifies each person who opens an account. Accordingly, when you register your Apple Cash Account and, as a result, your Apple Cash Balance, we will ask you for certain information, including, but not limited to, your name, street address, date of birth, your Social Security number, and other information that will allow us to identify you.

https://applecash.greendot.com/termsconditions/#tandc

Anti-money laundering regulations, know-your-customer financial regulations, and for tax compliance, most likely.

For details on some of the related regulations, start with the USA PATRIOT Act.