Because it is correct. In today's world you're pretty much forced to have a bank account open if you want to have a "normal" life, i.e. a life where you own a house (most probably via a mortgage), where you pay your bills (most probably online) and where you receive your salary (most probably via a bank account).

As such, the great majority of tax-payers are also bank customers, and this was not based on their own choosing (meaning they couldn't "afford" to avoid being bank clients). As such, banking customers bailing out failing banks de facto means tax-payers bailing out failing banks.