Because the fall of Han is a traditional demarcation point in Chinese historical periodisation.
The reason is actually less to do with the Han dynasty itself, than it is about what came afterwards. In traditional Chinese historiography, Han is followed by an era known as the "Wei-Jin-Northern and Southern Dynasties period" (魏晋南北朝)(1).
You see, when the Han Empire fell in c. 220, it marked the beginning of extended political divisions and, later, barbarian incursions that wrecked havoc in China. In this sense, it is somewhat analogous to the fall of Rome and the European Dark Ages. Other than a 50 year period under the Western Jin dynasty, China was not unified again until AD 589, 369 years later.
Because this was a period of intense instability and rapid changes, not just politically(2) but also socio-economically and demographically(3), it is usually given a separate treatment as its own topic. By logical necessity, therefore, the fall of Han concludes the pre-Wei/Jin period of classical Chinese history.
Your textbooks either followed longstanding conventions or just arrived at the same conclusion over where to end a chapter. However, it's probably only a coincidence that "all" your textbooks chose to demarcate Chinese history like that. Another fairly common scheme ends classical history at the unification of China under Qin in 221 BC, and then considers the Qin, Han and Wei/Three Kingdoms period together as one unit.
(1) Also known as the Six Dynasties though the two terms are not completely identical - the Six Dynasties refer to the six regimes that established their capital at Jianye (modern Nanjing).
(2) During this period, China was first divided into the Three Kingdoms, and then - following a series of nomad incursions - shattered into the "Sixteen Kingdoms" in the north and a "Southern Dynasty" behind the Yangtze River. The north eventually consollidated into a (Northern) Wei dynasty, only to then splintered into the Eastern and Western Wei. Both states were subsequently supplanted by the Northern Qi and Northern Zhou respectively. The Souithern Dynasty began originally as remnants of the Jin, but after a while was replaced by the Song, then the Qi, then Liang, and finally Chen.
(3) The barbarian migrations led to major demograaphical changes, for example the "Southern Voyage of Clothes and Crowns" (衣冠南渡) - an euphemism for the educated Han literati class of nothern China fleeing across the Yangtze River.