The usual argument for supporting the new military regime in Egypt is the same as the argument that was used for supporting the Mubarak regime (right up until it fell): Egypt needs stability. Secretary of State Clinton call Egypt "stable" two weeks before Mubarak was overthrown.
But like the old military regime the new one won’t be stable either, and today’s Washington Post explains one reason why in an article entitled "Egypt’s military expands it’s control of the country’s economy." Under Mubarak the generals had control of a large part of the economy. Here’s the Post:
Now, experts say, the Egyptian economy is increasingly shaped by the opaque desires of the ruling generals. And the military’s business activities appear to be expanding — from the manufacture of basic items such as bottled water and furniture into larger infrastructure, energy and technology projects, analysts say.
“We’re dealing with a brand-new economy that’s now run by ‘Military Inc.,’ ” said Joshua Stacher, an Egypt expert at Kent State University who has studied the military economy.
Several military regimes have actually followed policies that brought prosperity: Chile under Pinochet and the generals in South Korea are examples. But in those cases the military did not control parts of the economy and followed free-market policies. Egypt is very different: less of a commitment to the market, and huge segments of the economy that will be off limits to reform. This suggests that Egypt’s economy will not take off and will not provide the prosperity that Egyptians seek--and perhaps now expect.
So the most likely prospect is a military regime that crushes dissent, insufficient economic growth, leading to more dissent, leading to more repression. That is not, to say the least, a formula for stability.