The crisis engulfing the world’s oldest bank, Italy’s Banca Monte dei Paschi di Siena, has many causes, but its roots go back nine years to a lunch at a fancy Geneva hotel.

It was there, at the Four Seasons Hotel des Bergues, that three of Europe’s top bankers gathered to plot a hostile bid to buy and break up Dutch bank ABN Amro in what became the biggest bank takeover, worth €71 billion (then $101 billion).

The...