Casuistry

The false dawn had been implicated, its circularity
seen as a rebuke to honest folks, a third largest city
in the brain...

"Casuistry" is over-complex and disengenuous argumentation, maybe a "circular" or "false" argument? "To be implicated" in something is usually a bad thing. Hence there is a fear of being "found out," exposed to the scorn of "honest folk" who feel the very existence of such arguments is a rebuke to them, both because it isn't "honest" and because it's probably "over their heads." The phrase "honest folks" is itself a rebuke to such folks, because it is a cliché connoting a certain distance from anyone who would use the phrase about themselves.

...Others were quick to join
the fray. It wasn't our fault that so many
appeared specious in the waning light of February:
Who, indeed, would they appeal to?
There were no precedents for its apparent soundness,
not yesterday's dribs and drabs, the remnants
of someone else's feast, I'd wager...

There is a conflict or fray occuring. The "others" joining in are like personified arguments. After all, we don't usually call people "specious," speaking instead of "specious arguments." Here the royal "we" of the poem distances himself from potential allies, offering up casuistry with no possibility of appealing to a higher authority or precedent (note the legalese). The argument being proposed is apparently sound, but is not. The past, yesterday, is not a source of authority; there is no valued precedents, only a diminished things, dribs and drabs of someone else's past wealth.

...And what if
a lot of them come back and decide to settle down
with their parents, enraptured with home cooking
all of a sudden? Will they make the cut?

Here there is the possibility, or impossibility, of a return to a better past. Will the specious arguments return and live with their parents? This "home cooking" does not sound very appealing, so the word "enraptured" becomes very ironical. Obviously they won't "make the cut" because they went back to live with their parents, who are doubtlessly "honest folks." They have failed to change anything.

And what's out there for us on another
putative fine day? Oversubtlety? Our own quodlibets?

So the poetic "royal we" of the poem is stuck pretty much where he began, in oversubtle casuistry and ironic suspicion, "quodlibets" of no concern to anyone else. The day is not so fine if it is only "putatively" fine. It is the false dawn of the poem of the poem. He is no happier, no more successful than the "adult children" living at a home. Once "quick" to join something more lively but now complacently domestic. Here we have the typically Ashberian suburban melancholy, in which neither honesty nor irony come out smelling too good.