The Education is much more a record of Adams's introspection than of his deeds. It is an extended meditation on the social, technological, political, and intellectual changes that occurred over Adams's lifetime. Adams concluded that his traditional education failed to help him come to terms with these rapid changes, hence, his need for self-education. The organizing thread of the book is how the "proper" schooling and other aspects of his youth was time wasted, thus, his search for self-education through experiences, friendships, and reading.
Many aspects of the contemporary world emerged during the half-century between the Civil War and World War I, a half-century coinciding with Adams's adult life. An important theme of The Education is its author's bewilderment and concern at the rapid advance in science and technology over the course of his lifetime, sometimes now called Second Industrial Revolution, but incarnated in his term "dynamo". The Education mentions the recent discovery of X-rays and radioactivity, and shows a familiarity with radio waves in his citation of Marconi and Branly. Adams purchased an automobile as early as 1902, to make better use of a summer in France researching Mont Saint Michel and Chartres. He correctly predicted that the 20th century would have even more explosive changes. Adams repeatedly laments that his formal education, grounded in the classics, history, and literature, as was then the fashion, did not give him the scientific and mathematical knowledge needed to grasp the scientific breakthroughs of the 1890s and 1900s.
Two aspects set The Education apart from the common run of autobiographies. First, it is narrated in the third person; second, it is frequently sarcastic and humorously self-critical.
The Education repeatedly mentions two long-standing friends of Adams, the scientific explorer of the Far West, Clarence King, and the American diplomat, John Milton Hay.
The Education does not discuss Adams's marriage, and the illness and 1885 suicide of his wife, Clover; it skips 20 years from 1872 to 1892. Adams, splendidily reflective and self-critical in so many other ways, did not articulate what, if anything, he had learned from these sobering experiences. He did, though, reference his marriage in indirect ways. For example, he lamented how the memorial he had constructed for his wife had become something of a tourist attraction. More generally, his outlook clearly changed after her death.

Question: Why did Adams feel had to educate himself?
Answer: His formal education did not help him deal with the rapid changes in his life.
Alternative answer: His traditional education could not keep up with the rapid changes