There is no clear answer as to why the Japanese point to their nose when referring to themselves. Westerners also, probably cannot give a clear answer as to why they refer to themselves by placing the palm of their hand on their chest.
The differences in gestures may have arisen from the differences in the way the Japanese, American, and English perceive the nose
“Nose” appearing in idioms such as “look down one’s nose,” “turn up one’s nose,” and “to make a long nose” all carry a derogatory meaning in English and hence, nose has taken on an image that connotes rudeness. Standing the palm of the hand and fluttering it on the nose indicates contempt for the other.
Because it is located in the center of the face, nose in Japan was taken in the context of symbolizing pride as in the expression, hana ga takai meaning “to be proud of.” There are also other expressions such as hana de ashirau meaning “to treat a person with contempt” or “to look down on a person,” and hana ni kakeru meaning “to boast of.” But there are not nearly as many offensive expressions concerning the nose in Japanese as there are in English.
Until recent times, the expression hana sama used for oneself was derived from pointing to the nose to refer to oneself.