Think of it this way: you make $60k a year, but somehow borrow $1M to short a bunch of stock. Unfortunately, the market goes up, and margin calls come in on the $1M you borrowed. It doesn't matter that you can cover your living expenses with your salary (i.e. that you're cash-flow positive); the banks want their $1M back, and you don't have it. You're insolvent.
The situation in the banks is similar: there are collateral requirements that have to be met, trades with other banks that have to be honored, etc. A bank can cover its day-to-day operational expenses and be cash-flow positive, but if it suddenly has to pay someone else a big chunk of money that it doesn't have the liquid assets to provide, then it's still insolvent.
Actually, the terminology is a little different for financial firms than private traders.
Say that you take out a mortgage on a new house. The bank lets you borrow up to a certain percentage of the house's value, say 90%. The other 10% is a down payment that you must meet with your own money.
Now lets say the value of your house falls from $100,000 to $90,000. The way your mortgage is written, you probably still owe the bank $90,000 (90% of the original purchase price). However, the way debt contracts are written in the financial world, you would have to PAY the bank $9,000 to reduce your total borrowing to 90% of the CURRENT value of the property, or $81,000. That $9,000 payment is a "margin call" in financial market terminology.
So, financial firms borrow up to a certain amount of the assets that they lend, say 90%. If the value of those assets drops in half, and the value of mortgages plummeted on the open market, they owe their lenders enormous sums (45% of the value of the assets, for a 50% drop in value on 90% leverage).
Those margin calls forced a lot of firms out of business, even though their assets were still performing and still paying enough to meet their debt payments and operating expenses. If the firms could call their mortgages, they would be fine, but they can't because the mortgage money is spent on a house which is a non-liquid asset. The financial firms likely thought that their assets were undervalued on the market because of the panic that set in, but no matter. That's not the way their contracts were written.
So why is this the fault of mark-to-market? The banks knew the rules of the game, and they knew the terms of the contracts. They were speculating on asset appreciation, they got burned, and now they are bankrupt.
I thought about getting into this, but I was trying to keep the metaphor simple. But when you really think about it, the intent of the two systems are pretty similar: a mortgage is backed by a physical asset (a home) that is usually worth about as much as the debt that finances it (if not more), and can be liquidated to guarantee the debt if the borrower defaults. Stock investors have no equivalent physical assets to back their trades, and banks have established the margin-call system to compensate.