Final answer:
The Kaiser allowed the Reinsurance Treaty with Russia to lapse because he believed that Germany's strategic interests no longer aligned with maintaining the treaty, preferring to strengthen Germany's relationship with Austria-Hungary.
Step-by-step explanation:
The Reinsurance Treaty was a secret agreement between Germany and Russia to maintain neutrality should either country be involved in a war with a third nation. Kaiser Wilhelm II allowed the treaty to lapse in 1890 because he and his advisors believed that a close relationship with Russia was no longer necessary or beneficial to Germany's strategic interests.
This decision was influenced by a complex interplay of diplomatic, military, and domestic factors, including the Kaiser's desire to pursue a more aggressive foreign policy and his belief that the treaty was incompatible with Germany's alliance with Austria-Hungary.