Her brother complex may be the reason she rarely calls Rito "Onii-chan"; less a lack of respect and more a sign of her wish that their relationship was something other than that of a brother and sister.
She also states how she and Rito used to play together before Lala entered their lives.
The ending implies that his love troubles will continue on forever.
As Riko Yuusaki, his female alter-ego, she is a beautiful girl (with a physical appearance resembling a tomboy) who gets much attention from men, such as Motemitsu, the perverted principal and even Saruyama, Rito's best friend.
In contrast to her brother, she is very mature and does not hesitate to tease him, going as far as stating they aren't blood-related, but quickly retracting the statement, playing it off as a lie.
Mikan also seems to have a certain lack of respect for Rito because of this (she hardly ever addresses him by his honorific as an older brother), but does refer to him as "Onii-chan" as thanks for trying so hard to take care of her when she develops a fever and when he gives her a Christmas present.
Rito's nature is borderline clumsy, where he always ends up molesting or groping the many girls in the series (though mostly unintentionally).
Rito's independent and reliable 12-year-old sister, Mikan takes care of the housework while their parents are away on business and watches after Celine.Mikan even calls him a "playboy" (as does Nana) for attracting so many girls all of a sudden.Mikan, however, does respect Rito's relationship with Lala, even going so far as to tell Momo not to get too close to Rito for Lala's sake, although it is fairly obvious that she could have done this out of jealousy from how close Momo was getting to Rito.Mikan may not show it, but she cares very deeply for Rito and misses his company, to the point one could suspect her of having a brother complex.This is more evident in the second OVA where she wonders if he would marry her if they were not blood related, and in the manga where she blushes every time another character mentions her brother, and also in the 5th OVA where after being hit by the pollen she tries to molest him while affectionately calling him "Onii-chan".