By law, they have to have your SSN for managed payments. They are complying with U.S. Anti-money laundering regulations, specifically the Bank Secrecy Act and more specifically the Customer Identification Program requirement. All financial institutions (which include services beyond just banks) are required to identify and verify the identity of their customers. Part of that process involves obtaining your SSN.
Ebay is also required to have systems to protect your personal information, such as your SSN (this is called PCI Compliance). Those systems are independently audited at least annually, but breaches certainly do happen but less so than in the past. Breaches are usually at businesses that were storing your information when they didn’t need to be (and thus were not being audited for PCI compliance) – they should have relied on only the financial services party to have that info.
I've been selling on eBay for more than 20 years. Fact is, my social security number - and yours -- are probably available to about a jillion parties with all the data breaches we've had. And, yes, everybody and his brother is now or will soon be required to report about every penny they send you ...
I wasn't pleased when eBay announced their "Managed Payments" program, but truth is it's working out really seamlessly.
That said, I've told eBay many times and still maintain their "ethics" are best described as "Take the money and run!" Until something better comes along though, I'll stick with them (and their clearly idiot programmers, who still can't manage problems I've screamed about for years). Foreign buyers in particular greatly increase prices on many items I sell.
Dennis