Itsuki is the last member to have joined the SOS Brigade, having been recruited by Haruhi as a “mysterious transfer student.”
Itsuki is constantly smiling and always speaks in a formal and polite manner. He is also prone to giving long and detailed explanations, usually illustrated by exaggerated hand gestures. Itsuki has confirmed to Kyon once that his outer personality is merely an artificial image he fakes in accordance to Haruhi’s impression of him, and hints that his true character is something quite different, being “less pleasing” in the eyes of others. Maintaining his casual, constantly smiling self, however, is vital for keeping Haruhi’s mentality balanced.
Out of the three Brigade members, Kyon is the least fond of Itsuki. He often finds himself annoyed with Itsuki’s plastic smile, his willingness to acquiesce to Haruhi’s outrageous schemes, playful teasing and his various forays into his psychological and philosophical theories (e.g., omphalos hypothesis, Anthropic principle, etc.). He is also distrustful of Itsuki’s intentions, comparing him to Yuki Nagato when it comes to deciphering his expressions. Itsuki’s fondness for speculation often causes him to produce explanations for situations involving the SOS Brigade, its members and related events. Ironically, Itsuki can only share his theories with Kyon and also enthusiastically plays different kinds of board games with him to pass the time, despite losing all the time, although Kyon suspects that he may be doing so on purpose.
Itsuki was sent to observe and keep Haruhi emotionally stable, in order to protect the rest of humanity. Although he is an esper, which is exactly one of the sorts of people Haruhi desires to meet, Itsuki never reveals himself as such, at least, not to her.
Despite the theory he advances in which Haruhi is the equivalent of God, Itsuki says that there are many differing lines of speculation about Haruhi within “The Agency.” Itsuki himself does not believe in a singular God, nor does he regard Haruhi as such, although he reveals that he has colleagues that do. Apparently, most of the questions that he raises about Haruhi’s true nature are philosophical in nature and do not necessarily represent his personal beliefs. Itsuki also reveals that the majority of “The Agency” advocates observing Haruhi instead of doing anything that might provoke her.
In the Disappearance arc, the altered Koizumi reveals that he has a crush on Haruhi. This does not necessarily mean that the real Koizumi harbors such feelings, but it is possible that he would have feelings for her if Kyon would not be Haruhi’s love interest.
In the Astonishment arc, Koizumi is revealed to be the leader and founder of the Agency. Furthermore, he reveals part of his true personality when he blows up at the aliens and time travelers for meddling. More or less, he threatens war against both factions should they continuing tampering with Haruhi. Koizumi also says that he is a part of Haruhi’s subconscious made physical, although he never explains what he means more fully. He seems especially suspicious of the time travelers, particularly Asahina (Adult).