Explain why war broke out in 1914?

There is never any good reason for wars. An economist named Kondratieff analyzed market records going back 800 years and found a cycle, 35 to 70 years long, that included two distinct types of wars in every cycle. So the best reason anyone has found for a war is that it was time for one.

You can find analyses of wars at fee.org Here is one:
fee.org/articles/the-economics-of-war/