How did the Guarantee of Belgian Neutrality led to World War 1?

The Guarantee of Belgian Neutrality led to British involvement in WWI, but not to the outbreak of the war itself.

Briefly, in the 1860s Germany united into a single nation. This alarmed France, which picked a fight with Germany and lost, giving up Alsace and Lorraine in the peace. The French, humiliated, smarted for revenge, and made an alliance with Russia. Thus Europe's most repressive monarchy and its most republican state became allies. The obvious aim of this alliance was Germany. The German military then had to plan for a two front war, because war with either France or Russia meant war with both. What the German general staff arrived at was a plan to defeat France quickly, while the massive but ponderous Russians were still mobilizing their forces. In order to beat France quickly, the Germans decided to go around (outflank) the French frontier forts by going through Belgium and hooking into northern France.

The 1839 Treaty guaranteeing Belgian Neutrality was signed by four Great Powers, including Britain and Prussia. Germany was a successor state to Prussia, and the former Prussian dynasty was now the German dynasty. The Treaty was binding on Germany. Nevertheless the Germans made the cynical decision to invade Belgium on their way to France, in the event war began. And, they would do so even if the war which began was a war with Russia, which was what happened in 1914. When the Germans invaded Belgium the British reminded them of their obligations under the Treaty and demanded they withdraw from Belgium. The German Foreign Minister scornfully denounced the Treaty as "a scrap of paper". Shortly thereafter Britain was at war.