Note that the asset/liabilities are reversed from the perspective of the bank versus the customer.
A simple way to have the sensitivity you describe is if the bank pays variable interest on deposits while making fixed rate loans. If rates rise, they pay more on deposits while loan rates are unchanged. In such a case the net interest margin shrinks.
You could read a few quarterly reports from banks to see how they discuss margins and profitability. Sample link below.
If anyone could explain this to me it would be great.
If a company's liabilities are more sensitive to interest rate changes what would the impact on Net Interest Margin be if rates increase?