He's a lunatic. He's overly optimistic, easily excited, and extremely emotional. He has his own "Corner of Woe," and he spends much of his day sulking in that aforementioned corner. He's eccentric, loud, and obnoxious too.
So, with all of these negative traits, why does she put up with his antics? Why does she let him hang on her every word as though she is preaching some great truth? Why does she change her words in order to revive him from his woeful state? Why does she follow along with his insane plots? Why does she let him baby her and save her from the terrible twins' staged wrath? Why does she allow him to envelope her in his painfully tight embrace on a daily basis?
Because there is also a different side to him, a side that is endearing and loveable. There is a side that only his friends see and understand. This side is different from the host persona that he shows the young ladies who frequent the Host Club. This side is his true self, and he is unafraid to show her this side. He trusts her to understand him without judgement.
She accepts him and his idiosyncrasies, because he is also stunningly sweet, gracefully gentle, and ever so enthusiastic. He is innocent, naïve, and trusting. He's helpful, loving, and honest. He is affectionate (though sometimes suffocatingly so) and he has a beautiful soul.
It's this side of him, Tamaki Suoh, that she loves. She knows that he is never hiding anything from her. She knows what he is thinking by simply glancing into his violet eyes, and he trusts her with his thoughts.
And because she loves that side of him, she has learned to also adore his traits that aren't so perfect.
Because she doesn't love part of him. She loves all of him, his faults included.
Because she loves who he is.