The separation of single-walled carbon nanotubes (SWNTs) according to their electronic structure has attracted much recent attention. In many cases, metallic SWNTs are separated from semiconducting SWNTs and enriched in the supernatant due to stronger interaction between metallic SWNTs and adsorbates. However, the inverse separation of semiconducting from metallic SWNTs is often observed. In this computational study, the underlying mechanism is elucidated by density functional theory. We show that the shape of an aromatic molecule, the degree of hybridization between a molecule and a SWNT, and the oxidative state of SWNTs can affect the type of enriched SWNTs. In principle, one can control the type of enriched SWNTs by selecting a structurally compatible aromatic molecule or changing the hole concentration of the SWNTs.