Before the 22nd Amendment, presidents generally limited themselves to seeking only two terms because of the precedent set by George Washington, who only served two terms, declining to run for a third term. It would not be a leap to suppose he would be successful in such an attempt- the Electoral College elected him unanimously to both terms he served. After that, it became an unwritten rule of sorts, as much of Washington's presidency was. Being the first president, he established many precedents, the two term tradition among them. Respect for Washington and the precedents he set is part of the answer to your question.

Another part of the answer is fear of tyranny. In a letter to the Legislature of Vermont in 1807, Thomas Jefferson said, "if some termination to the services of the chief Magistrate be not fixed by the Constitution, or supplied by practice, his office, nominally four years, will in fact become for life." So, lacking a constitutional restriction or a restriction imposed by tradition on number of terms, he believed the presidency could become a life-long position (even though terms were set to four years).

Therefore, in this regard, it was politically taboo as the social custom was generally against it and prevented it. However, social customs change.

Examining those who ran for third terms and why they failed also sheds light on the answer to your question. Ulysses S. Grant had significant support for a third term in 1880, but many Republicans did not wish to see him reelected and implied he was power hungry. Beyond this accusation, he was also weakened as a candidate by the corruption which had plagued his presidency. So, while the fact he was seeking a third term did become an issue, there were other factors which influenced his failure to receive the Republican nomination.

Which brings us to Theodore Roosevelt, who you mentioned, who also sought a third term unsuccessfully in 1912, his main opponents Woodrow Wilson and Taft, who was his chosen successor but fell out of favor with T. Roosevelt. Dissatisfied, T. Roosevelt decided to seek the Republican nomination himself and, when he did not receive it, ran as the Progressive (Bull Moose) Party candidate. Woodrow Wilson emerged the victor in 1912. However, it seems the third term attempt was not necessarily what caused T. Roosevelt to lose- he was, and remains, the best performing third-party presidential candidate in United States history, receiving 29% of the popular vote and 88 votes in the Electoral College. His loss largely attributable to the fact the Republican Party was divided between T. Roosevelt's progressives and Taft's conservatives, preventing either from consolidating sufficient support to win, allowing Wilson to win with just 42% of the popular vote. This, T. Roosevelt's loss is more attributable to a three-way contest than his attempt for a third-term (In fact, he pledged he wouldn't run for a third term seemed to be more of an issue than the third term itself).

In 1920, Wilson too hoped to receive the Democratic nomination, despite his failing health. As with earlier candidates, this means there were other issues at work in his failure other than he was seeking a third term. Many also saw the United States' involvement in WW1 as a breaking of his 1916 promise to stay out of war. Detractors also pointed to his failure to involve members of Congress in the formation of the Treaty of Versailles.

With Franklin D. Roosevelt, the two-term tradition was finally broken. Indeed, he was elected to not three, but four terms. He sought a third term because he saw it as his duty to continue leading his nation as WWII began in Europe. The third term was an issue in the 1940 election, but he defeated his opponent, Wendell Willkie, with 449 Electoral votes to Willkie's 82. His fourth term was justified by the war- he urged voters not to "change horses midstream."

FDR's success points to, that while the "taboo" of a third term was an oft-mentioned issue, the voters were willing to ignore that taboo for the right candidate or the right reason. It was not an insurmountable obstacle; the tradition was sufficiently weak by FDR's time it could be argued it was no longer truly taboo.

As you noted, the 22nd Amendment placed a constitutional prohibition on 3rd terms, removing the issue of taboo altogether.

Another perspective is that many presidents would not desire a third term even if offered, as Obama indicated he would not desire a third term even if it was allowed- so the tradition of two terms and fear of tyranny may not have played as significant roles in every pre-22nd Amendment president's decision not to seek a third term.

Thank you for your interest in United States history, and good luck with your further studies!

Sources: Washington http://www.history.com/this-day-in-history/washington-unanimously-elected-by-electoral-college-to-first-and-second-terms http://www.mountvernon.org/digital-encyclopedia/article/presidential-precedents/ Jefferson http://teachingamericanhistory.org/library/document/letter-to-the-legislature-of-vermont/ Grant https://www.nytimes.com/learning/general/onthisday/harp/0605.html T. Roosevelt http://millercenter.org/president/biography/roosevelt-campaigns-and-elections http://www.usnews.com/news/articles/2008/01/17/three-way-race-of-1912-had-it-all http://millercenter.org/ridingthetiger/bull-moose-campaign-1912 Wilson https://www.britannica.com/event/United-States-presidential-election-of-1920 FDR http://www.history.com/this-day-in-history/fdr-nominated-for-unprecedented-third-term http://millercenter.org/president/biography/fdroosevelt-campaigns-and-elections https://www.britannica.com/event/United-States-presidential-election-of-1940 http://blog.constitutioncenter.org/2015/11/fdrs-third-term-decision-and-the-22nd-amendment/ 22nd Amendment http://blog.constitutioncenter.org/2015/02/today-in-constitutional-history-presidents-are-limited-to-two-terms-in-office/ Modern/Obama http://nypost.com/2015/07/28/obama-confident-hed-win-a-3rd-term-if-he-could-run/