I thought I had a eureka moment for 2023, where I would take a one-way to europe and then book a series of round trips back to the US in order to save a substantial amount of money - but it appears impossible to do this. I thought maybe it was a Schengen/EU thing but I've tried multiple combinations and it keeps spitting out errors.

For example this fall I'm returning MUC-CDG-CVG in late September and then heading back CVG-JFK-ARN a few weeks later. These flights have seats available. I'm already on them, but I can't book MUC-CVG-ARN. Is this a citizenship issue or do they know what I'm trying to do and blocking it?

It's a fare combination restriction in DL (and other Skyteam member) fares and is found in the fare rules in the "Combinability" section of the rules. Open jaws ex-EU must originate and return to same country. Something like MUC-CVG-FRA would be permitted, but not your itin because MUC and ARN are in different countries. It's been discussed here a few times before.

https://www.flyertalk.com/forum/33907303-post6.html

I believe I read something here on flyertalk about the "open jaw to different countries" being a problem, but I don't know how you'd find that thread.

Fiddlesticks.

This might still work but it would require some trains or short hops.

Star Alliance allows those kinds of open jaws but apparently not Skyteam.
This past May flew MCO-EWR-VIE and returned ARN-FRA-MCO, all on one ticket and it priced as a roundtrip/open jaw, not as two one-way fares.

That�s a totally different scenario and would certainly be possible on Skyteam.

HAM/BER and ARN connect by train and by plane, so lots of options making a MUC-CVG-HAM/BER scenario work for you. Or, if this works better, GOT/MMX-CVG-ARN.

Different situation. That's a US-origin booking and DL/Skyteam fares also allow open jaws from different countries on the EU end (Area 2) for US-origin fares just like the other alliances. Note that when you book a roundtrip/open-jaw ex-US, they apply US-origin fares in both directions and these can be completely different from fares for trips which originate in a different country/region.
UA/Star fares generally don't allow open jaw on the EU end for cheapest ex-EU fares unless it's within the same country (they have the same "one country" restriction for EU end in the Combinability section as DL ex-EU fares). But they have slightly higher priced ex-EU fares that allow open jaw in Area 2 region which can be combined on one ticket. There's no upfare path for DL/Skyteam ex-EU fares and you can only book as one-way tickets on separate fares if you want an open jaw in different countries on the EU end when starting your trip in the EU.

This all makes a lot of sense now. I knew it was possible to do but it's because I originally looked a few months ago for MUC and FRA RTs since I go there most often and I sort of treat Germany in general as my basecamp when traveling to Europe. Starting this fall things just happen to be different and that's when I discovered it wasn't this easy to do.

You guys have given me some food for thought. Thank you.