To summarize: it's some kind of big Mexican standoff between Italian politicians, banks, pensioners, German politicians, and Brussels. Or a big game of chicken.

If the banks go insolvent- bad for account holders (many Italian voters), Italy's economy, and by extension the whole eurozone.

If the bank is bailed out by current EU rules, bond holders have to participate in the bailout by absolving some of the bonds. This is meant to prevent profiteering off bailouts. But bank bonds are a popular 'safe' investment for pensions. So nobody wants to be accused of screwing their own constituents. And of course it's all the taxpayers who pay for the bailout in the end.

Or they can change the rules, and bail then out without touching the bonds, which the Italian prime minister wants. His leverage if that if EU rules hurt pensioners, he will almost certainly be replaced by someone very anti EU. But rules are rules to the Germans, and they are very interested in keeping the EU rules strong in the Brexit aftermath.

  "Laugh about it, shout about it
  When you've got to choose
  Ev'ry way you look at it, you lose"