There are many stories on the origins of Tai Chi, most of which try to link the modern forms to some ancient source. But there are a few, more recent, events that are perhaps more relevant.
All modern Tai Chi has been impacted by two major events: The fall of the Qing Dynasty and the Communist Revolution.
By the time Yang Luchan had developed his style of Tai Chi in the 1840s and 50s, the Qing dynasty was already on the way out. The First Opium War of 1839 was a major defeat of the Chinese Navy by the British. The foreign colonial powers had proven that the old Dynasty, and the old Chinese way, were powerless in the face of modern Western technology.
Throughout China, resentment against the Western powers and the religion they were importing, Christianity, was growing. Secret societies dedicated to preserving the old ways developed. Groups like the Society of Righteous and Harmonious Fists paved the way to the Boxer Rebellion of June 1900. These societies mixed prayers, martial arts, and training in an effort to preserve traditional Chinese values.
Yang Luchan died 30 years before the Boxer Rebellion, but there is no doubt that he had first hand experience of the troubles rocking China at the turn of the century. In the employ of the ethnically Manchu Qing Dynasty, he surely felt the disquiet of the mostly Han population, and the dismay they must have felt at the sight of a rotting empire crumbling before Western invaders.
Yang Style Tai Chi grew within a cauldron of conflicting trends. The need for revitalizing Chinese society was become evident to everyone. In 1861 the government launched the Self-Strengthening Movement, an official policy of national industrialization. In the private sphere, the Chinese adopted the Western ideals of physical health (echoed in the secret societies and the Boxers).
Similarly, Chinese intellectuals delved back into the ancient roots of Chinese culture as a bulwark against the rising pressure of Christianity. Taoism made a come-back. It is easy to see how upper class Manchu would turn to a physical practice with claims to an ancestral Chinese pedigree. Like Tai Chi.
And in turn Tai Chi gained the input of learned Taoist philosophers, who were able to infuse the martial art with a solid Taoist foundation. Because up until then, most martial arts were developed in rural villages as a means of defending themselves from roaming brigands. Like Chen style Tai Chi.
What separates Chen style and Yang style Tai Chi is the input of an educated, urban, Taoist elite.
The Qing Dynasty fell in 1911, leading to a new Republic which promptly fell apart. The chaos of the following years, including civil wars, popular uprisings, the Japanese invasion and World War II, shattered the traditional relationships between master and students. All the social norms which had shaped traditional Chinese martial arts training were gone.
It was small wonder that the Communist Revolution ushered in the Cultural Revolution. The Great Leap Forward was supposed to be a break from a culture that had seemed incapable of standing up to the Western powers. When pushed, the Empire crumbled. Mao Zedong tried, with disastrous results, to change that.
The Cultural Revolution was a body blow to the traditional Chinese martial arts. It is hard to over-emphasize the damage done to ancient, traditional knowledge. Master Wang Yannian decided to pass on his knowledge of the Yangjia Michuan Style when he saw how few students were left. The knowledge was on the verge of disappearing for good.
In the 60s and 70s the Chinese government tried to repair some of the damage done and created sport academies to teach some of these traditional martial arts. But many of the more esoteric, Taoist aspects were stripped. The health and sport aspect were emphasized. In the case of Tai Chi, it essentially ceased to be a martial art.
Unless the more traditional, pre-Cultural Revolution forms are found and preserved.