Deposit insurance causes inflation because (the quantities of) demand deposits affect the price cash and banks are able to issue liabilities in excess of their reserves as a consequence of the Government guarantee. Because the market expects monetisation, the bank is able to issue many liabilities without apparent consequence.
In free market circumstances, the deposits would not be allowed to rise above the available reserves because deposits (accounts) would be withdrawn and deposits would diminish. Government intervention prevents this process, allowing deposits to rise. There is no incentive for the customers to act early, in withdrawing funds, because the latecomers will get the same. It prevents a bank run. Deposit insurance enables the banking system to cause inflation.
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