Why were tanks less effective in mountainous, forested, swampy, and built-up terrain?

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armoured vehicle A British Warrior mechanized combat vehicle serving in NATO's Stabilization Force in Bosnia and Herzegovina, 1997.

Tanks are primarily designed as offensive instruments that achieve their full potential in broad, open plains, such as those found in northern France or southern Russia. Their effectiveness is significantly diminished in mountainous, forested, swampy, or built-up terrain due to two primary factors:1

Diminished Trafficability: These environments often present physical obstacles that restrict the movement and mobility of armoured vehicles.1
Lack of Deployment Space: Such terrain often lacks the necessary room for tanks to maneuver and deploy effectively as a cohesive force.1

In these challenging environments, tanks are frequently reduced to a secondary role, serving primarily to support infantry rather than acting as the primary spearhead of an offensive. Furthermore, when tanks are used as stationary artillery in these areas, they are often less effective than specialized field cannon because their rotating turrets must be designed to absorb the recoil of their guns, which typically limits the calibre of the weaponry they can carry.1