I know a little bit about Theodore Roosevelt and how he apparently introduced some important progressive reforms, but most of what you hear about him in culture is related to him being some sort of paragon of masculinity. It’s always about him bare knuckle boxing, or getting shot but still giving his speech because bullets don’t dissuade him, or riding horses and hunting in the wilderness out west. Where did this idea of him as the ultimate manly man come from? Why him instead of, say, Abraham Lincoln, who was not from a blue blood family and was actually from the frontier? Would he still be a famous president just based on his accomplishments (I don’t know a ton of them?) And is any of this actually accurate?
This is a very intriguing question. Overall, there are a few things that go into answering this question, some partially deal about the man himself, and others are about the way in which history is remembered and retold. Really, a discussion on Teddy the man and Teddy the historiography.
To start off, Teddy did have an intresting life. He came from a wealthy and politically powerful family, went to a prestigious and connected school (Harvard University), served as the Assistant Secretary of the Navy, left that to join a war, came back to be Governor of New York, became Vice President, and became the youngest person to hold the office of President (not elected, mind you, since he took over after the assassination of William McKinley). Outside of that, he had a love for hunting, conservation, and as said boxing. He also had a racist outlook and the inferiority of blacks. Take this quotation from paragraph four:
while Roosevelt's administration was not supportive of civil rights for blacks. The popularity of eugenics and the philosophy of social Darwinism reached a zenith during the early part of century, and racism was integrated into presidential party platforms as late as the early 1930s. President Roosevelt believed blacks were intellectually inferior, and began to decrease the number of federal appointments to blacks and promised Southerners that he would appoint local federal officials that would not disrupt the accord between north and south.
He also helped to create the framework for the FDA and responded to America's disgust at the conditions of food processing as expressed in the book "The Jungle" by Upton Sinclair.
Roosevelt was a man of his time, but was also a character. His advocating for trust-busting made him a hero to many who saw the gilded age as a golden age for worker exploitation. While he himself, also worked to expand the power of American capitalism. But, he also gave himself to the creation of mythos. Roosevelt wrote... a lot. Kathleen Dalton writing in The Journal of the Gilded Age and Progressive Era mentions that Roosevelt wrote over 20 books and tens of thousands of letters. He very much helped to shape his own image and he was very successful at it.
Outside of his own promotion, Roosevelt was seen as emblematic of the Gilded age and Progressive era. Even though he broke from the Republican party leadership in the 1912 election, Teddy was still a very good symbol of Republican politics and popularity that was heavily used for party purposes. To this day, in public opinion polls, Teddy ranks frequently in the top 5 for presidents, and almost always in the top 10. That type of name recognition and approval is going to be frequently used and also attract attention to the man. Furthering the building and repeating of his character and myths.
As to the second point, in the writing of history, there was and sometimes still is, a tendency to write of historical figures in these sweeping and grandiose ways. This is generally referred to as Great Man History. An idea that history was shaped by great men and their actions. During the course of writing, the object (a human who impacted historical events) starts to undergo a change. From a simple human being of flesh and blood, an untouchable larger than life creation whose actions are almost preordained. The distance of time from the person's life to the time of writing starts to add to the mythologizing. While people were lived around the same time as the figure in writing pass away, their ability to recount stories of them and humanize figures starts to disappear. As a personal anecdote, I try to read journals of contemporary figures and others as much as possible to try and break through passed down mythologies about historical figures and to see how and what people thought about them during their lifetime and time of their actions.
Overall, Teddy was rich, powerful, educated, rugged, a soldier, a writer, a leader, a follower, a reformer. America's renaissance man president. Partially because of his own making, partially because of his own actions, partially because of public love for charismatic leaders, Teddy's mythos was made.
I'd add, Kathleen Dalton's " Theodore Roosevelt: A Strenuous Life " (Knopf 2002) is worth the read, as is as many digitized copies of Roosevelts letters and diaries as you can find.
I hope this helps, If you have any follow up questions I'll try to help!