It's overly-brief so I can't really discern a legal theory, and I'm not a lawyer, but basically the argument seems to be going something like this:
-The government generally indicates an interest in fostering competition (particularly via laws such as the Sherman Act, among other ways). This has popped up in some cases, where the gov't has required an airline to break up a hub or divest gates at a few airports due to over-dominance (IIRC UA had to dump some gates at EWR, AA at DCA, etc.) to allow a merger to go through.
-Removing another airline (VX, in this case) would reduce competition without a redeeming benefit to consumers.
--This wouldn't necessarily be a bad thing, but the airline industry is already over-consolidated and it's not like VX was about to collapse, so there was really no reason to allow any further merger.
--VX and AS also have just enough overlap on the West Coast that you'd be pulling out at least some competition of note in several markets within the region.
-Finally, the only reason we're facing the present situation is because of the royal fiasco surrounding SRB's shares at the roll-out.
The hangup, of course, is that VX, AS, and B6 (walk into a bar...) are all a bit under-sized compared to the "big four" (due to the aforementioned mergers), so you can make a case either way in terms of competition (AS+VX has a strong base on the west coast which might well allow it to grow into a "fifth major", and I personally feel that there is/was a case for a three-way tie-up between all three...something which I do expect to stumble out eventually as I frankly think it'll be a cold day in Helena before there's anymore merging "up top": The sorts of slot reallocation you'd have to orchestrate to avoid a hurricane of "lockout hubs" would make the sorts of contortions the Feds tried during the formation of Conrail look straightforward. Honestly, if I'm the Feds I'd be terrified about what would happen if one of the four majors were to start falling apart. On the other hand, AS-VX might be a hair too strong on the West Coast in some respects.
So is there a case against the AS-VX merger? Possibly. Will it prevail? Lord only knows, but it at least has room to muck up the merger. Hell, even if it fails maybe we'll get lucky and this mess will tie the merger up in court for a few years.