Personally, the facet of Chinese history that grates me the most is the pretense that China has a ~2200 year history of successive unitary states (I'm not going to take pre-Qin unification as credible).
When you compare Chinese history to European history, there's a lot more parallelisms than you might expect from the popular conception. The Qin unification in 221BC is fairly contemporaneous with the rise of Rome in the west (who dispatched the Carthaginians in 201BC and the remnants of the Macedonians by 146BC). The Han dynasty collapsed around AD184 (with the Yellow Turban Rebellion), which stabilized into a three-way (later two-way) partition by AD220 that lasted until Sui reunification in 589; this unification persisted until the collapse of the Tang dynasty in 907. Similarly, in the West, the Roman Empire collapses in the Crisis of the Third Century (235-284), and reemerges in a mostly permanent state of division between Western and Eastern Empires. The Eastern Empire persisted until its defeat in 1204, whereas the Western Empire disintegrated over the 4th and 5th centuries but recoalescing into a Merovingian dynasty (Clovis I reunited most of modern France and Germany by his death in 511, although it was promptly divided on his death) and later a unified Carolingian kingdom that became the Holy Roman Empire when crowned by the pope in 800. Although the empire again divided on Charlemagne's death, it did stabilize as a Kingdom of France in the west and a HRE in the east, with a contested bit in the middle.
When you compare Chinese history to European history, there's a lot more parallelisms than you might expect from the popular conception. The Qin unification in 221BC is fairly contemporaneous with the rise of Rome in the west (who dispatched the Carthaginians in 201BC and the remnants of the Macedonians by 146BC). The Han dynasty collapsed around AD184 (with the Yellow Turban Rebellion), which stabilized into a three-way (later two-way) partition by AD220 that lasted until Sui reunification in 589; this unification persisted until the collapse of the Tang dynasty in 907. Similarly, in the West, the Roman Empire collapses in the Crisis of the Third Century (235-284), and reemerges in a mostly permanent state of division between Western and Eastern Empires. The Eastern Empire persisted until its defeat in 1204, whereas the Western Empire disintegrated over the 4th and 5th centuries but recoalescing into a Merovingian dynasty (Clovis I reunited most of modern France and Germany by his death in 511, although it was promptly divided on his death) and later a unified Carolingian kingdom that became the Holy Roman Empire when crowned by the pope in 800. Although the empire again divided on Charlemagne's death, it did stabilize as a Kingdom of France in the west and a HRE in the east, with a contested bit in the middle.