What I've noticed in comments on the internet, specifically DailyKos, is that "I think" serves as a prompt to contradiction, while "I believe" gets a pass, so to speak. I don't think this is conscious. Rather, some minds perceive thought as a challenge that they need to refute.
A half century ago when I was in school, we were taught that using the first person is improper. But, in the political arena it is not only accepted, but expected. Perhaps the combination with belief, rather than thought, which is, after all, speculative and tentative, represents a compromise that doesn't so much withstand challenge as negate it. Belief is hard to argue with. That's why the religious rightists have an advantage. They don't have to compete to win; they just excise the opposition.
Winning by exception or getting ahead by cutting the competition out. It's sort of like pruning a fruit tree. The U.S. is an exceptional culture. It is ruled by exception. Congress, quite naturally, follows the pattern. Given five options, or however many come up, Congressmen rule all but one out, so the "last man standing" wins the contract or the appointment without anyone having to make a positive choice. The exception not only "proves the rule," the exception rules.
"Eenie, meenie, miney, mo ...."
It seems there's a new version in a song by Sean Kingston and Justin Bieber