https://www.federalreserve.gov/monetarypolicy/reservereq.htm
_No_ bank has the ability to handle all of their depositors pulling their money out at the same time. I'm not sure how many could handle 25% + however many pulled in the preceding days either.
Bank runs caused banks to default because the banks have run out of cash, plenty of banks have failed despite having sufficient assets to cover their depositors.
An easy way to understand this, imagine a teeny tiny bank:
* 100k cash on hand
* 10 customers with 50k deposits
* 100 customers with 100k mortgages
This bank has 10 million in assets, and 500k in debt, so has 9.5million in net assets
Now 2 customers withdraw 30k each, you still have 9.5 million in net assets but you only have 40k cash. So you sell one of the mortgages at a discount to get some cash on hand. You lose 10k and you report that you did that, and now you have say $130k cash again. But now some of your customers friends hear that some people withdrew a lot of their money, and that you're selling things at a loss so they go oh no, I'm going to with draw all my money. So 2 customers come in to withdraw their money and you say "we don't have enough cash to do that", so you get a super expensive loan and start trying to sell more assets at increasing discounts. People see you doing that and go "oh shit" and now all of your depositors come to get their cash. You have now sold of a bunch of your assets at potentially steep discounts, have some very expensive credit, and still can't give people their deposits back. Congratulations on experience a bank run.
Because of this your bank is now legally insolvent and is seized by the government despite clearly having more assets than debt, you are unable to service that debt.
Alternatively consider someone with a mortgage. They have a property worth $X, and a debt of $(X-Y). Now imagine the bank comes to them and says "you need to pay back your mortgage in 24 hours or we will seize all your property". You can see how that might cause problems no matter how much of their mortgage had been paid off.
In the real world banks have lots of other things set up to reduce risk, but the core principle is the same. No significantly sized bank can handle a full bank run - that's why things like the FDIC were created: it means most people don't have to worry that if they don't immediately pull their money from the bank they'll lose all their money, and so they don't panic withdraw, and so reduce the risk of a run-induced bank failure.
What happened here is that SVB was apparently endeavoring to rebalance its (in fairness terrible) asset mix and was taking a loss on doing so. But that spooked a bunch of billionaire VCs who instructed all the startups they were funding to withdraw from SVB, which caused other VCs to do the same, and pretty soon all these companies with assets far beyond the FDIC limit and/or completely uninsured _they_ did have a reason to fear losing their money if the bank failed. That triggered a run, and because it was actual companies the size of the withdrawals were far more than any well run bank would ever expect to suddenly need so the result was inevitable.
Just to add, I would expect the big US and international banks, and probably most of the slightly smaller and mid sized ones as well, to be able to weather a run from individuals but I don't think any bank in the world could handle all their corporate clients simultaneously demanding all their assets as cash in the space of only a day or so.
[edit: HN ate the formatting on teeny bank so I've added moar newlines]
This kind of event is ostensibly prevented by regulations requiring "shock testing" of banks, but the GOP and trump rolled back those regulations for banks like SVB because government regulation is bad, and the CEO of SVB told congress that despite the established history of unregulated banks failing just like this, it would not happen again because magic.
I guess that's why we have the FDIC, and why banks pay into the insurance. And why 2008 wasn't as bad as the crash that led to its creation. It looks like the fund has $124 billion as of 2022.
https://www.fdic.gov/news/press-releases/2022/pr22064.html
That doesn't sound like enough to do much more than cover $250k on all accounts, but I guess that's the idea.