The advantage of a blockchain is that it's distributed - many people verify changes, so changing it after the fact is pretty much impossible. Running a blockchain ledger with a single party in control would mean they can rerun all of the transactions and rewrite the blockchain from any given point, so there'd be no way for other people to trust it. Consequently, unless Facebook shared access to the blockchain with other people, there would be absolutely no advantage at all.
Plus, they would have to get rid of all edit/delete features. Sounds like a nightmare to me. Can they create an FB coin? Sure but the use of a centralized payment system goes against blockchain...
The obvious answer to your question is that they're looking into using it for the sake of expanding their online payment system. Sending money between users with Messenger is something I've read of (but haven't ever come across, maybe because here where I live (IT/EU) it mightn't be enabled).
The slightly more disturbing answer is that they've latched-on to some of the arm-waving about blockchain technology being the future of distributed computing (or something like that), specifically an enabler for storing one's social data in a distributed environment and therefore prospecting the idea of social graphs being distributed onto blockchain thus obsoleting their current business model, and have therefore decided to investigate this technology, see if they can somehow insinuate themselves into the role as a centralising force, and/or have decided to develop it so they can patent it and use that patent defensively to protect their current business model.
[0] https://en.wikipedia.org/wiki/Unified_Payments_Interface
A company’s stance on blockchain can also serve as a test of a company’s management. In my view, companies pushing blockchain technology (e.g. IBM, Microsoft, Intel, Oracle) are disconnected from customers’ actual needs and have mediocre management. Companies that don’t talk about blockchain (e.g. Facebook, Amazon, Google, Apple) are more likely to produce sensible technology that will work in the real world.
https://glennchan.wordpress.com/2018/02/20/blockchain-is-a-u...