The Belgian route rested on a short-war assumption

Why did German planners choose the Belgian route despite the risk of British intervention?

They expected a short war, judged Russia too large to defeat quickly, and treated a rapid western victory through Belgium as the more plausible option.

German planners believed they needed to defeat either France or Russia quickly. Russia's size made a rapid eastern decision seem less plausible, which left a sweep through Belgium as the route to a fast victory over France. Recent short conflicts, especially the Franco-Prussian War, encouraged the wider expectation that another European war would also end quickly. The choice becomes easier to understand once that assumption is restored, even though the resulting violation of Belgian neutrality carried severe diplomatic costs.