Generally speaking this has to do with various fare buckets and advance fares. That $339 F fare might not be bookable two weeks from the date of flight and the $559 fare might be. Note the dates in my screenshots for an example.




(That second screenshot does indeed show F as $10 cheaper than upgradeable Y, this Y fare is a fare that would be immediately upgradeable for an MVPG.)

Generally speaking airline inventory management is pretty sophisticated, and has to account for "a seat that flies empty accounts for $0 in revenue" as well as "we have the ability to upgrade expensive coach fares immediately into F as well as sell some of our 16 F seats on this flight on this day for cheap, and it might be wise to do so", as well as "government employees or corporate accounts can sometimes buy expensive Y fares but are prohibited from buying F, we might want to upgrade an elite who does this though since it might incentivize them to buy those expensive coach fares".

You'll see them doing this sort of pricing and go "LOL, they're idiots, why would you price coach more than first?", and basically not understand why they're doing what they are doing.