Addendum: 

The way it hurts banks is that as interest rates in general rise, their depositors start moving their money to places that pay better interest rates. As with Silicon Valley Bank, this results in the bank having to sell assets for less than book value (such that the purchaser can obtain current market interest from them) and accept a loss on their accounting books. Once this happens a couple of times, banking regulators notice that the bank's capital position is starting to weaken. 

Essentially, the losses start eating into the shareholders' equity and the bank's operating funds. Investors start selling the stock and depositors who may have more than the FDIC protected amount in that bank start trying to move their excess funds. This in turn requires more asset sales.

Banks could push Certificates of Deposit with tough lockup clauses, but no one is going to do that for 1-2% APR.