The reasons are strategic, and go well beyond the old feud with the Nationalists, who fled to Taiwan and set up a rival government when the Communists defeated them on the mainland in 1949. Extending its sovereignty to Taiwan would give China control of waters far into the Pacific Ocean, including sea lanes used to move military and cargo shipments between U.S. allies Japan and South Korea. Beijing also believes that if Taiwan is not united with China, it eventually could turn against the mainland. In this scenario, an unfriendly Taiwan could provide a massive beachhead for hostile forces. Moreover, China's view is that that if Taiwan is not united with mainland China, eventually, then it could turn against Beijing.
China clearly dwarfs Taiwan, but China looks at the picture in reverse.
Stretching almost 250 miles north to south, Taiwan sits just across the straits from Fujian province, China's most economically developed coastal region. Taiwan also controls the islands of Quemoy and Matsu, both little more than a stone's throw from the mainland coast. If you're a PLA general it is your mission in life to advance the recovery of Taiwan. But despite Beijing's threats to take Taiwan by force if it tries to assert its independence, most military experts agree that China is still not equipped to invade successfully, and probably won't be for several years. Taiwan, after all, is armed to the teeth with the help of the U.S. military technology, whereas China is coming from far behind in its military modernization.