So Jims example was that spy activities leads to his wife throwing all his belongings on the lawn. Is that conflict? Because of course he could be ready for a divorce anyway and if all his stuff is on the lawn, it's just that much easier to get to! So this is part of the conversation, then, where we just keep asking why every answer is a problem until the heat death of the universe.
Why is it a problem for Andy to be innocent in prison? Why's it a problem that guards threaten him and inmates rape him? Why's it a problem that he doesn't like those things?
I think the question of should only refer to the setup of "X is a problem." The answer then is the proof that X is a problem, but not another problem in itself.
For instance, we know it's a problem for Andy to be innocent in jail because he tries to escape, or because he's threatened by the guards, or because some of the inmates rape him. We know it's a problem for the spy to Prove he's good because his stuff ends up on the lawn. Or because the neighbors get mad, or because he's going to miss the Christmas party.
But why are those things problems? They're not. And even if they are problems, it's not about why that answer is a problem now. It's just about proving that the setup is a problem. If there's anything else to show in order to prevent anyone from assuming a problem i'd think it would just need to be illustrated in the story.
If this spy is the only one merrily wishing other's a Merry Christmas and wearing festive (some might say ugly) Christmas sweaters on missions, and setting up the office Secret Santa gift exchange, then the audience will see that missing the Christmas party is what makes proving himself a good spy a problem. If we see him ignoring his wife's angry cussing while gathering secret documents off the front lawn, then the audience knows he's not okay with his stuff being easier to get to.
(Sorry, I think I've veered off topic a bit, and maybe got a bit convoluted in some of that as well, and I'm not even done yet! You can blame a slow morning at this office for this long post)
As far as the thing that cannot co-exist I'd say that proving ones self a good spy cannot co-exist with leaving at 5pm on the dot and making it in time for Secret Santa. Or proving ones self a good spy cannot co-exist with having happy neighbors. It's not world-ending conflict, but there's still conflict between those things, isn't there?